CN104182574A - concrete mixing blade design method based on spiral angle linear variation - Google Patents

Abstract

The invention discloses a concrete mixing blade design method based on spiral angle linear variation and belongs to the field of construction machinery design. A spiral-line blade designed by the method has fine fitting property and meets the requirements on blade stirring and unloading, the spiral angles of the spiral stirring blades in different cylinders are in relationship of linear variation, smooth transition of the spiral lines in different cylinder is realized at the cylinder combination, and the continuity of the spiral line is guaranteed. The spiral angle and shape of the blade can variate from the cylinder mouth to the cylinder bottom according to the function of the cylinders. The concrete can be prevented from bonding in the positions effectively, and the working efficiency of a concrete stirring truck can be improved effectively.

Description

Based on the method for designing of linear change helix angle concrete stirring vane

Technical field

The invention belongs to building machinery design field, relate to a kind of method for designing based on linear change helix angle concrete stirring vane.

Background technology

For the method for designing of truck mixer helical blade, a kind of is to introduce in conical section the concept of calculating cone, calculate the upper log spiral that adopts of cone, then, to calculate cone as the helix with reference to calculating cylinder inboard wall, point out the variation linear approximate relationship of cylinder inboard wall helix helix angle; But, because this method is not pointed out the mathematical law of non-isogonism log spiral to implement more complicated.The research having in addition thinks, in the time that the helixangleβ in log spiral expression formula is constant, this expression formula is log spiral, and in the time that helixangleβ is a variable, this expression formula is non-isogonism log spiral; But can know by checking, when helixangleβ is that variable is expressed as by β after the function of spiral corner Fa, β can not change by given funtcional relationship, and namely helixangleβ is uncontrollable, be helix starting point helix angle determine after, the end helix angle that can not get designing in advance.

Summary of the invention

The deficiency existing for prior art, the invention provides a kind of method for designing based on linear change helix angle concrete stirring vane, and it can be taken into account, and blade stirs and the performance requirement of discharging, has ensured the continuity of helix.

For achieving the above object, technical scheme of the present invention is as follows:

A kind of method for designing based on linear change helix angle concrete stirring vane of the present invention, blade changes at the bottom of from nozzle to cylinder continuously, comprises the steps:

The first step: according to plane isogonism log spiral R=R ₀× e ^{k θ}, according to its character k=cot β, the relational expression drawing:

R'/R＝k＝cotβ (1)

Wherein, R is utmost point footpath, and θ is polar angle, R ₀for initial utmost point footpath, set R ₀=1, k is constant, and β is helix angle, and R' represents that R is to θ differentiate, and e is mathematics Euler's constant, is the truth of a matter of natural logarithm function;

Second step: by changing its K value, its span is 0.25～0.36 according to formula (1), to change helixangleβ, setting cone section cylinder nozzle is minor diameter place, and the cylinder end is major diameter place, and the k value of establishing each section of cylinder nozzle and cylinder bottom is k _j, j=1,2,3 ... n+1, the hop count that n is churn, n>=3 and n are integer, setting the initial k value of nozzle cone section blade is k ₁, cylinder base cone section blade finishes k value for k _n+1, and k _n+1> k ₁, make k ₁with k _n+1along cylinder axis direction linear change, the interconversion rate PP that obtains k value edge cylinder axis direction is:

$\mathrm{PP}=\frac{k_{n+1}-k_1}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i}---\left(2\right)$

Wherein N _i, i=1,2 ... n, represents each section of cylinder axis direction length;

Determine that according to formula (2) each section of cylinder is at the k of junction value k _j, that is: j=2,3 ... n:

$k_j=k_1+\mathrm{pp}\×\left(\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{N}_i\right)---\left(3\right)$

The 3rd step: set D _lfor the diameter of churn nozzle, the cylinder end and each section of cylinder junction, l=1,2 ... n+1; Set inner cone section R _2m-1for utmost point footpath corresponding to nozzle, inner cone section R _2mfor utmost point footpath corresponding at the bottom of cylinder; Base cone section R _2n-1for utmost point footpath corresponding at the bottom of cylinder, base cone section R _2nfor utmost point footpath corresponding to nozzle, make the k value of each cone section cylinder along utmost point footpath R direction linear change, obtain each cone section cylinder k value rate of change P _m:

$P_m=\frac{k_{m+1}-k_m}{R_{2m}-R_{2m-1}},m=\mathrm{1,2}\·\·\·n,m\≠n-1---\left(4\right)$

In formula: inner cone section: $R_{2m-1}=\frac{D_m}{2\sin {\mathrm{\η}}_m},R_{2m}=\frac{D_{m+1}}{2\sin {\mathrm{\η}}_m},$

Base cone section: $R_{2n-1}=\frac{D_n}{2\sin {\mathrm{\η}}_n},R_{2n}=\frac{D_{n+1}}{2\sin {\mathrm{\η}}_n},$

η _mfor the circular cone element line angle of each cone section, m=1,2 ... n, m ≠ n-1,

Obtain the conical section helix differential equation according to formula (1) and formula (4):

$\frac{R^{\′}}{R}=k_m+P_m\×(R-R_{2m-1})---\left(5\right)$

K _mrepresent the initial k value of each cone section cylinder, that is: m=1,2 ... n, m ≠ n-1;

Cylindrical section cylinder blade curve adopts variable slope curve to replace log spiral, and the slope using the k value of cylindrical section cylinder as developed curve, makes k value linear change vertically; Obtain

Cylindrical section cylinder k value rate of change: $P_{n-1}=\frac{k_n-k_{n-1}}{N_{n-1}}---\left(6\right)$

Obtain the cylindrical section helix differential equation according to the funtcional relationship of formula (6) and rate of curve:

$\frac{\mathrm{dy}}{\mathrm{dx}}=k_{n-1}+P_{n-1}y---\left(7\right)$

The 4th step: the helix equation that is obtained each cone section cylinder by formula (5) is:

$\frac{R}{R+k_m/P_m-R_{2m-1}}=\frac{P_m\×R_{2m-1}}{k_m}\×e^{\left({\mathrm{\θ}-\mathrm{\θ}}_m\right)\×(k_m-P_m\×R_{2m-1})}---\left(8\right)$

By formula R=R ₀× e ^{k θ}, R ₀=1, obtain in formula m=1,2 ... n, m ≠ n-1;

The helix equation that is drawn cylindrical section cylinder by formula (6), (7) is:

$y=\frac{k_{n-1}}{P_{n-1}}\×(e^{P_{n-1}\×x}-1)---\left(9\right)$

Wherein x, y are plane coordinate system direction, and x is along cylindrical drum diametric(al), and y is cylindrical drum axis direction, and x is independent variable, and y is dependent variable.

Further, when described each section of blade shape is different, according to the respectively helix equation of the section of cone tin and cylindrical section cylinder of blade, calculate the coordinate of blade each point:

Taking the nozzle center of circle of churn as true origin, taking the central axis of churn as Z axis, and with feedstock direction for just, adopt cylindrical-coordinate system taking Z axis as dead axle line, the coordinate of radial direction represents with W, and rotation angle represents with Fa, taking degree as unit, and press left hand helix direction rotation

The parameter expression mode of helical blade under this coordinate system is: be selected in a moving some A on barrel, the spiral curve of blade is drawn in this variation with helical blade rotation angle Fa on barrel,

According to formula (8), taking θ as independent variable, R is dependent variable, and conversion obtains the trajectory equation of moving some A on cone section cylinder and is:

$R=\frac{(\frac{k_m}{P_m}-R_{2m-1})\×\frac{P_m\×R_{2m-1}}{k_m}\×e^{(\mathrm{\θ}-{\mathrm{\θ}}_m)\×(k_m-P_m\×R_{2m-1})}}{1-\frac{P_m\×R_{2m-1}}{k_m}\×e^{(\mathrm{\θ}-{\mathrm{\θ}}_m)\×(k_m-P_m\×R_{2m-1})}}---\left(10\right)$

Wherein: m=1,2 ... n, m ≠ n-1,

In formula, θ is the corresponding polar angle of curve while launching along cylindrical shell, and unit is radian, and the transformational relation of it and rotation angle Fa is:

$\frac{\mathrm{\θ}-{\mathrm{\θ}}_m}{D_m/R_{2m-1}\×180}\×\frac{180}{\mathrm{\π}}=\frac{\mathrm{Fa}}{360},---\left(11\right)$

Wherein m=1,2 ... n, m ≠ n-1,

Abbreviation obtains:

$\mathrm{\θ}=\frac{\mathrm{Fa}\×D_m\×\mathrm{\π}}{R_{2m-1}\×360}+{\mathrm{\θ}}_m---\left(12\right)$

Be positioned at the some a on spiral curve for inner cone section helical blade, corresponding to Fa, the parameter coordinate of its Z axis and radial direction is (Za, Wa); According to formula (10), (12), show that the coordinate expression formula that on blade, a is ordered is:

$\left\{\begin{array}{c}\mathrm{Za}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right),m=1\\ \mathrm{Za}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1},m=2,\·\·\·,n-2\end{array}\right.---\left(13\right)$

Wa＝R×sin(η _m) (14)

Wherein m=1,2 ... n-2,

Get two middle breaks for inner cone end blade, be respectively b, c, be respectively (Zb, Wb), (Zc, Wc) corresponding to the b of Fa, the coordinate that c is ordered, coordinate expression formula convolution (13), (14):

$\left\{\begin{array}{c}\mathrm{Zb}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+H1,m=1\\ \mathrm{Zb}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+H1,m=2,\·\·\·,n-2\end{array}\right.---\left(15\right)$

Wb＝R×sin(η _m)-K1 (16)

Wherein m=1,2 ... n-2,

$\left\{\begin{array}{c}\mathrm{Zc}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+S,m=1\\ \mathrm{Zc}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+S,m=2,\·\·\·,n-2\end{array}\right.---\left(17\right)$

Wc＝R×sin(η _m)-K2 (18)

Wherein m=1,2 ... n-2,

H1, K1, K2, S are empirical value, and span is respectively: H1=20-80mm, K1=70-120mm; K2=280-350mm; S=0-30mm;

D is vane tip arbitrfary point, is (Zd, Wd) corresponding to the d point coordinate of Fa, coordinate expression formula convolution (13), (14):

$\left\{\begin{array}{c}\mathrm{Zd}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+S-H2,m=1\\ \mathrm{Zd}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+S-H2,m=2,\·\·\·,n-2\end{array}\right.---\left(19\right)$

Wd＝R×sin(η _m)-K3 (20)

Wherein m=1,2 ... n-2,

H2, K3 are empirical value, and span is respectively: H2=60-100mm, K3=400-440mm;

Helical blade in base cone section, do not get break, blade is γ with the angle of cylinder diametric(al) line, span is: γ=10-24 °, be respectively (Za, Wa), (Zd, Wd) corresponding to the blade bottom arbitrfary point a of Fa and the coordinate of arbitrfary point, top d, convolution (10), (12), show that the coordinate expression formula that a is ordered is:

Za＝N ₁+…+N _n-(R-R _2n)×cos(η _n) (21)

Wa＝R×sin(η _n) (22)

D point is with respect to the height B of a along cylinder axis direction linear change, and its expression formula is

$\left\{\begin{array}{c}B=K3-\frac{K3-K4}{N_4-G}\×(\mathrm{Za}-N_1-N_2-N_3),N_1+N_2+N_3\≤\mathrm{Za}\≤N_1\≤N_2+N_3+N_4-G\\ B=K4-\frac{K4-K5}{G}\×[\mathrm{Za}-(N_1+N_2+N_3+N_4-G)],\mathrm{Za}\≥N_1+N_2+N_3+N_4-G\end{array}\right.---\left(23\right)$

In formula, K4, K5, G are empirical value, and span is respectively: K4=280-320mm, K5=150-200mm, G=180-240mm; Convolution (21), (22), (23), show that the coordinate expression formula that d is ordered is:

Zd＝N ₁+…+N _n-(R-R _2n)×cos(η _n)-B×Tan(γ) (24)

Wd＝R×sin(η _n)-B (25)

In cylinder barrel segment, the trajectory equation of moving some A is identical with formula (9) helix equation, that is:

$y=\frac{k_{n-1}}{P_{n-1}}\×(e^{P_{n-1}\×x}-1)---\left(9\right)$

Taking x as independent variable, y is dependent variable

Wherein the transformational relation of x and Fa is:

$x=\frac{\mathrm{\π}\×D_{n-1}}{360}\×\mathrm{Fa}---\left(26\right)$

Cylindrical section cylinder helical blade is positioned at the some a on spiral curve, and corresponding to Fa, the parameter coordinate of Z axis and radial direction is (Za, Wa); Convolution (9), (26), show that the coordinate expression formula that a is ordered is:

Za＝N ₁+…+N _n-2+y (27)

Wa＝D _n-1/2 (28)

Get a break b for cylindrical section cylinder helical blade, the coordinate of ordering corresponding to the b of Fa is respectively (Zb, Wb), its coordinate figure expression formula convolution (27), (28):

Zb＝N ₁+…+N _n-2+y+H1 (29)

Wb＝D _n-1/2-K1 (30)

D is vane tip arbitrfary point, is (Zd, Wd) corresponding to the d point coordinate of Fa, and convolution (27), (28) show that the coordinate expression formula that d is ordered is:

Zd＝N ₁+…+N _n-2+y+S (31)

Wd＝D _n-1/2-K3。(32)

Further, the rotation angle Fa changing method of described blade: in the time determining the 1st section of blade rotary angle Fa to n-1 section cylinder, Fa all since 0 ° of variation, sets intermediate variable: M at each section of cylinder tube port position ₁, M ₂..., M _n-2, recording the rotation of each section of cylinder blade screw line to the rotation angle Fa actual numerical value at the bottom of each section of cylinder cylinder, each section of cylinder blade rotary angle Fa actual numerical value expression formula be, that is: Fa _real:

The 1st section: Fa _real=Fa

The 2nd section: Fa _real=Fa+M ₁

………

N-1 section: Fa _real=Fa+M _n-2

Wherein Fa increases since 0 according to step-length successively at each section of cylinder, sets change step ii, that is: Fa=Fa+ii, until each section of cylinder blade screw line rotation is at the bottom of each section of cylinder cylinder;

Tail cone section cylinder, i.e. n section cylinder, rotation angle Fa changing method:

The anglec of rotation that to set Ta be tail cone section cylinder blade at the bottom of changing to tin from nozzle, Ta increases according to step-length successively from 0, draws rotation angle Ta when blade screw line arrives cylinder bear building-up bundle, is designated as M _n, in the time determining Fa, according to the rotation angle M drawing _n, the Fa making is from reducing successively according to step-length to nozzle at the bottom of cylinder, and Fa=Fa-ii, until be 0, sets intermediate variable M _n-1, record blade screw line and rotate to the rotation angle Fa actual numerical value at the bottom of the last period cylinder cylinder, tail cone section cylinder Fa actual numerical value expression formula is:

N section: Fa _real=M _n-1+ M _n-Fa.

Further, described change step ii is greater than 0 degree and is less than or equal to 20 degree.

Further, in both sides, described each section of cylindrical shell junction, transition section region is set, the blade arc joint in the each section of cylinder in blade arc two ends, described transition section region and both sides seamlessly transits.

Further, when described cylinder hop count is four sections of cylinders, its method for designing of the 1st section to the 2nd section is: that 1. sets this transition section region is respectively GD1 and GD2 along axial length; 2. determine horizontal ordinate Za1 and the Za2 of circular section, transition section edge and blade intersection point, Za1=N ₁-GD1, Za2=N ₁+ GD2; 3. the top point d ordinate with respect to Za1 and Za2 is determined in convolution (13), (20), in the 1st section of cylinder, is: $\mathrm{Wd}1=(\frac{\mathrm{Za}1}{\cos {\mathrm{\η}}_1}+R_1)\×\sin {\mathrm{\η}}_1-K_3,$ In the 2nd section of cylinder, be: $\mathrm{Wd}2=(\frac{\mathrm{GD}2}{\cos {\mathrm{\η}}_2}+R_3)\×\sin {\mathrm{\η}}_2-K_3;$ 4. determine the linear rate of change of ordinate of top point d, for show that the top point d ordinate expression formula that transition section changes is: Wd=Wd1+ △ 1[Za-(N ₁-GD1)], the horizontal ordinate that d is ordered calculates according to formula (19); 5. a, b, c point horizontal stroke, ordinate calculate according to formula (13)-(18) in transition section;

The method for designing of the 2nd section to the 3rd section is: that 1. sets this transition section region is respectively GD3 and GD4 along axial length; 2. determine horizontal ordinate Za3 and the Za4 of circular section, transition section edge and blade intersection point, Za3=N ₁+ N ₂-GD3, Za4=N ₁+ N ₂+ GD4; 3. determine the horizontal ordinate rate of change with respect to the break c of Za3 and Za4: the horizontal ordinate expression formula of the break c that draws variation in transition section: Zc=Za+S+ △ 2 × [Za-(N ₁+ N ₂-GD3)], c point ordinate calculates according to formula (18) in the 2nd section of cylinder, and in the 3rd section of cylinder, expression formula is: Wc=D _n-1/ 2-K2,4. determines the d point horizontal ordinate rate of change with respect to Za3 and Za4, the horizontal ordinate expression formula of the top point d that draws variation in transition section: Zd=Za+S-H2+ △ 3 × [Za-(N ₁+ N ₂-GD3)], and convolution (13), (20), (32) draw the ordinate of d point with respect to Za3 and Za4: in the 2nd section of cylinder, be: $\mathrm{Wd}3=(\frac{N_2-\mathrm{GD}3}{\cos {\mathrm{\η}}_2}+R_3)\×\sin {\mathrm{\η}}_3-K_3,$ In the 3rd section of cylinder, be: $\mathrm{Wd}4=\frac{D_{n-1}}{2}-K3;$ Thus, determine the linear rate of change of ordinate of the top point d of transition section variation, for the ordinate expression formula of the top point d that draws variation in transition section: Wd=Wd3+ △ 4[Za-(N ₁+ N ₂-GD3)]; 5. a, b point horizontal stroke, the coordinate figure of ordinate in transition section calculate according to formula (13)-(16) in the 2nd section of cylinder, in the 3rd section of cylinder, calculate according to formula (27)-(30);

The method for designing of the 3rd section to the 4th section is: that 1. sets this transition section region is respectively GD5 and GD6 along axial length; 2. determine horizontal ordinate Za5 and the Za6 of circular section, transition section edge and blade intersection point, Za5=N ₁+ N ₂+ N ₃-GD5, Za6=N ₁+ N ₂+ N ₃+ GD6; 3. determine the horizontal ordinate rate of change with respect to the break b of Za5 and Za6: the horizontal ordinate expression formula of the break b that draws variation in transition section: Zb=Za+H1+ △ 5 × [Za-(N ₁+ N ₂+ N ₃-GD5)], b point ordinate calculates according to formula (30) in the 3rd section of cylinder, and in the 4th section of cylinder, convolution (22) obtains expression formula: Wb=R × sin (η _n)-K1

4. determine the d point horizontal ordinate rate of change with respect to Za5 and Za6, the horizontal ordinate expression formula of the top point d that draws variation in transition section: Zd=Za+S-△ 6 × [Za-(N ₁+ N ₂+ N ₃-GD5)], and convolution (21), (23), (25) and (30) draw the ordinate of d point with respect to Za5 and Za6: in the 3rd section of cylinder, be:

in the 4th section of cylinder, be:

$\mathrm{Wd}6=(\frac{N_4-\mathrm{GD}6}{\cos {\mathrm{\η}}_4}+R_8)\×\sin {\mathrm{\η}}_4-[K3-\frac{K3-K4}{N_4-G}\×\mathrm{GD}6];$ Thus, determine the linear rate of change of ordinate of the top point d of transition section variation, the ordinate expression formula of the top point d that draws variation in transition section: Wd=Wd5+ △ 7[Za-(N ₁+ N ₂+ N ₃-GD5)]; 5. a point horizontal stroke, the coordinate figure of ordinate in transition section, calculates according to formula (27), (28) at the 3rd section, calculates according to formula (21), (22) at the 4th section;

In above-mentioned each step: Za draws according to the calculation expression of a point horizontal ordinate on each section of helical blade.

Further, when described cylinder is three sections of cylinders, determine transition section region according to the method for designing of the 2nd section to the 3rd section and the 3rd section to the 4th section described in claim 5.

Further, described blade is discharge blade and the blade that is connected with feed pipe in the feed pipe punishment of prostomum section, and setting feed pipe mouth of pipe place diameter is Dg1=470-500mm, and pipe end diameter is Dg2=480-510mm, and feed pipe length L g is: $\mathrm{Lg}=\frac{2\×K3-D1+\mathrm{Dg}2}{2\tan {\mathrm{\η}}_1},$

The method for designing of its discharge blade is:

Setting the length of discharge blade in tubular axis direction is Zg, Zg=170-210mm, elemental height is Ko, Ko=140-160mm, stopping height is K3-K2 with the distance of feed pipe outer wall, gets 1 break b, on blade, the coordinate expression way of each point a, b, c is respectively: a (Za, Wa) point coordinate value is calculated according to formula (13), (14), and b (Zb, Wb) point coordinate expression formula is:

$\mathrm{Zb}=\mathrm{Za}+\frac{H1\×\mathrm{Za}}{\mathrm{Zg}+S}$

$\mathrm{Wb}=\mathrm{Wa}-\frac{K1-\mathrm{Ko}/2}{\mathrm{Zg}+S}\×\mathrm{Za}-\mathrm{Ko}/2$

Blade tip c point with respect to a point height B 1 expression formula is:

$\begin{array}{c}B1=\frac{\mathrm{Za}+\mathrm{Za}/(\mathrm{Zg}+S)\×S}{\mathrm{Zg}}[\frac{D_1-\mathrm{Dg}1}{2}-K3+K2-(\mathrm{Zg}-H2)\frac{\mathrm{Dg}2-\mathrm{Dg}1}{2\mathrm{Lg}}-\mathrm{Ko}]\\ +\mathrm{Za}\tan {\mathrm{\η}}_1+\mathrm{Ko}\end{array}$

C (Zc, Wc) point coordinate expression formula is:

$\mathrm{Zc}=\mathrm{Za}+\frac{\mathrm{Za}}{\mathrm{Zg}+S}\×S$

Wc＝Wa-B1

The blade design method that is connected with feed pipe is:

Its length L of blade that is connected with feed pipe is: L=Lg-Zg, on blade, get two break b, c, on blade, the coordinate expression way of each point a, b, c, d is respectively: a (Za, Wa) point, b (Zb, Wb) point coordinate value is calculated according to formula (13), (14), (15), (16)

C (Zc, Wc) point coordinate expression formula is:

Zc＝Za+S

Wc＝Wa-B2+K3-K2

Blade tip d point with respect to a point height B 2 expression formulas is:

$B2=\frac{D_1-\mathrm{Dg}1}{2}+\mathrm{Za}\×\tan {\mathrm{\η}}_1-[\mathrm{Za}-(H2+S)]\×\frac{\mathrm{Dg}2-\mathrm{Dg}1}{2\mathrm{Lg}}$

D (Zd, Wd) point coordinate expression formula is:

Zd＝Za+S-H2

Wd＝Wa-B2。

Further, described GD1～GD6 span is respectively 150-400mm.

The invention has the beneficial effects as follows:

1. the stirring vane that adopts helix equation of the present invention to make, has good matching performance.Adopt the present invention to be out of shape the stirring vane of shape, there is more superior joint fairness, and aspect the homogeneity stirring, the remaining rate of discharging all tool have an enormous advantage.

2. the present invention is in the design of the discharge blade at discharge nozzle place, and discharging speed is fast, is difficult for forming buildup.

3. the present invention can take into account the performance requirement of blade stirring and discharging, and make the helix angle of different cylinder section inside spin stirring vanes be linear changing relation, helix in so different cylinder section forms and seamlessly transits in cylindrical shell junction, ensure the continuity of helix, also can effectively avoid concrete to bond in such position.Can effectively improve the task performance of truck mixer.

Brief description of the drawings

Fig. 1 is one-piece construction schematic diagram of the present invention.

Fig. 2 is tube structure parameter schematic diagram of the present invention.

Fig. 3 is each section blade profile shape schematic diagram of the present invention.

Fig. 4 is that churn structure helicoid bus of the present invention turns the coordinate schematic diagram of putting on face projection and blade.

In figure: 1. stirring vane; 2. inner cone section first paragraph cylindrical shell; 3. inner cone section second segment cylindrical shell; 4. stage casing cylindrical tube; 5. rear cone section cylindrical shell, 6. feed pipe.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Embodiment 1: as shown in Figure 1, the present invention is for the design of concrete stirring vane, and the helix angle of blade and blade shape can be according to each section of cylinder functions, the continuous variation at the bottom of realizing from nozzle to cylinder, and can seamlessly transit each section of cylindrical shell junction.

The present invention includes following steps:

The first step: according to plane isogonism log spiral R=R0 × e ^{k θ}, according to its character k=cot β, the relational expression drawing:

R'/R＝k＝cotβ (1)

Wherein, R is utmost point footpath, and θ is polar angle, R ₀for initial utmost point footpath, set R ₀=1, k is constant, and β is helix angle, and R' represents that R is to θ differentiate, and e is mathematics Euler's constant, is the truth of a matter of natural logarithm function;

Second step: as shown in Figure 2, by changing its K value, K value span is 0.25～0.36 according to formula (1), to change helixangleβ, setting cone section cylinder nozzle is minor diameter place, and the cylinder end is major diameter place, and the k value of establishing each section of cylinder nozzle and cylinder bottom is k _j, j=1,2,3 ... n+1, the hop count that n is churn, this example is selected n=4, and setting the initial k value of nozzle cone section blade is k ₁=0.25, cylinder base cone section blade finishes k value for k ₅=0.32, make k ₁with k ₅along cylinder axis direction linear change, the interconversion rate PP that obtains k value edge cylinder axis direction is:

$\mathrm{PP}=\frac{k_{n+1}-k_1}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i}---\left(2\right)$

Wherein N _i, i=1,2 ... n, represents each section of cylinder axis direction length, this example

N ₁＝1600mm，N ₂＝1000mm，N ₃＝1200mm，N ₄＝1200mm；

Determine that according to formula (2) each section of cylinder is at the k of junction value k _j, that is: j=2,3,4:

$k_2=k_1+\mathrm{pp}\×\left(\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{N}_i\right)=k_1+\mathrm{pp}\×N_1$

$k_3=k_1+\mathrm{pp}\×\left(\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{N}_i\right)=k_1+\mathrm{pp}\×(N_1+N_2)$

$k_4=k_1+\mathrm{pp}\×\left(\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{N}_i\right)=k_1+\mathrm{pp}\×(N_1+N_2+N_3)---\left(3\right)$

The 3rd step: as shown in Figure 2, set D _lfor the diameter of churn nozzle, the cylinder end and each section of cylinder junction, l=1,2 ... n+1; Set inner cone section R _2m-1for utmost point footpath corresponding to nozzle, inner cone section R _2mfor utmost point footpath corresponding at the bottom of cylinder; Base cone section R _2n-1for utmost point footpath corresponding at the bottom of cylinder, base cone section R _2nfor utmost point footpath corresponding to nozzle, make the k value of each cone section cylinder along utmost point footpath R direction linear change, obtain each cone section cylinder k value rate of change P _m:

$P_m=\frac{k_{m+1}-k_m}{R_{2m}-R_{2m-1}},m=\mathrm{1,2}\·\·\·n,m\≠n-1---\left(4\right)$

In formula: inner cone section: $R_{2m-1}=\frac{D_m}{2\sin {\mathrm{\η}}_m},R_{2m}=\frac{D_{m+1}}{2\sin {\mathrm{\η}}_m},$

Base cone section: $R_{2n-1}=\frac{D_n}{2\sin {\mathrm{\η}}_n},R_{2n}=\frac{D_{n+1}}{2\sin {\mathrm{\η}}_n},$

η _mfor the circular cone element line angle of each cone section, m=1,2 ... n, m ≠ n-1,

That is: $P_1=\frac{k_{m+1}-k_m}{R_{2m}-R_{2m-1}}=\frac{k_2-k_1}{R_2-R_1}$

$P_2=\frac{k_{m+1}-k_m}{R_{2m}-R_{2m-1}}=\frac{k_3-k_2}{R_4-R_3}$

$P_4=\frac{k_{m+1}-k_m}{R_{2m}-R_{2m-1}}=\frac{k_5-k_4}{R_8-R_7}$

In formula: $R_1=\frac{D_1}{2{\sin \mathrm{\η}}_1},R_2=\frac{D_2}{2{\sin \mathrm{\η}}_1},R_3=\frac{D_2}{2\sin {\mathrm{\η}}_2},R_4=\frac{D_3}{2\sin {\mathrm{\η}}_2},R_7=\frac{D_4}{2\sin {\mathrm{\η}}_4},$

$R_8=\frac{D_5}{2\sin {\mathrm{\η}}_4},{\mathrm{\η}}_1=\arctan \frac{|D_2-D_1|}{2N_1},{\mathrm{\η}}_2=\arctan \frac{|D_3-D_2|}{2N_2},{\mathrm{\η}}_4=\arctan \frac{|D_5-D_4|}{2N_4}$

This routine D ₁=1150mm, D ₂=2040mm, D ₃=D ₄=2348mm, D ₅=1800mm;

Obtain the conical section helix differential equation according to formula (1) and formula (4):

$\frac{R^{\′}}{R}=k_m+P_m\×(R-R_{2m-1})---\left(5\right)$

K _mrepresent the initial k value of each cone section cylinder, that is: k ₁, k ₂, k ₃, k ₄;

Cylindrical section cylinder blade curve adopts variable slope curve to replace log spiral, and the slope using the k value of cylindrical section cylinder as developed curve, makes k value linear change vertically; Obtain

Cylindrical section cylinder k value rate of change: $P_{n-1}=\frac{k_n-k_{n-1}}{N_{n-1}},$ That is: $P_3=\frac{k_4-k_3}{N_3}---\left(6\right)$

Obtain the cylindrical section helix differential equation according to the funtcional relationship of formula (6) and rate of curve:

$\frac{\mathrm{dy}}{\mathrm{dx}}=k_{n-1}+P_{n-1}y=k_3+P_{3}y---\left(7\right)$

The 4th step: the helix equation that is obtained each cone section cylinder by formula (5) is:

$\frac{R}{R+k_m/P_m-R_{2m-1}}=\frac{P_m\×R_{2m-1}}{k_m}\×e^{\left({\mathrm{\θ}-\mathrm{\θ}}_m\right)\×(k_m-P_m\×R_{2m-1})}---\left(8\right)$

By formula R=R ₀× e ^{k θ}, R ₀=1, obtain in formula m=1,2 ... 4, m ≠ 3;

The helix equation that is drawn cylindrical section cylinder by formula (6), (7) is:

$y=\frac{k_{n-1}}{P_{n-1}}\×(e^{P_{n-1}\×x}-1)=\frac{k_3}{P_3}\×(e^{P_3\×x}-1)---\left(9\right)$

Wherein x, y are plane coordinate system direction, and x is along cylindrical drum diametric(al), and y is cylindrical drum axis direction, and x is independent variable, and y is dependent variable.

According to this routine helix equation, stirring vane can have multiple design, and this example adopts the constant screw type blade design method of existing blade shape to design.

Embodiment 2: the screw type blade that this example adopts blade shape to change, each section of cylinder blade profile shape as shown in Figure 3.According to the respectively helix equation of the section of cone cylinder and cylindrical section cylinder of embodiment 1 Leaf, calculate the coordinate of blade each point; In the time that described each section of blade shape is different, concrete grammar is:

With reference to Fig. 4, taking the nozzle center of circle of churn as true origin, taking the central axis of churn as Z axis, and with feedstock direction for just, because blade is helicoid state in cylinder, so adopt the cylindrical-coordinate system taking Z axis as dead axle line, the coordinate of radial direction represents with W, and rotation angle represents with Fa, to spend as unit, and press left hand helix direction rotation

The parameter expression mode of helical blade under this coordinate system is: be selected in a moving some A on barrel, the spiral curve of blade is drawn in this variation with helical blade rotation angle Fa on barrel,

According to formula (8), taking θ as independent variable, R is dependent variable, and conversion obtains the trajectory equation of moving some A on cone section cylinder and is:

$R=\frac{(\frac{k_m}{P_m}-R_{2m-1})\×\frac{P_m\×R_{2m-1}}{k_m}\×e^{(\mathrm{\θ}-{\mathrm{\θ}}_m)\×(k_m-P_m\×R_{2m-1})}}{1-\frac{P_m\×R_{2m-1}}{k_m}\×e^{(\mathrm{\θ}-{\mathrm{\θ}}_m)\×(k_m-P_m\×R_{2m-1})}}---\left(10\right)$

In formula, θ is the corresponding polar angle of curve while launching along cylindrical shell, and unit is radian, and the transformational relation of it and rotation angle Fa is:

$\frac{\mathrm{\θ}-{\mathrm{\θ}}_m}{D_m/R_{2m-1}\×180}\×\frac{180}{\mathrm{\π}}=\frac{\mathrm{Fa}}{360},---\left(11\right)$

Wherein: m=1,2,4, abbreviation obtains:

$\mathrm{\θ}=\frac{\mathrm{Fa}\×D_m\×\mathrm{\π}}{R_{2m-1}\×360}+{\mathrm{\θ}}_m---\left(12\right)$

Be positioned at the some a on spiral curve for inner cone section helical blade, corresponding to Fa, the parameter coordinate of its Z axis and radial direction is (Za, Wa); According to formula (10), (12), show that the coordinate expression formula that on blade, a is ordered is:

$\left\{\begin{array}{c}\mathrm{Za}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right),m=1\\ \mathrm{Za}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}=(R-R_3)\×\cos \left({\mathrm{\η}}_2\right)+N_1,m=2,\end{array}\right.---\left(13\right)$

Wa＝R×sin(η _m) (14)

Wherein m=1,2 ... n-2=1,2,

Described inner cone section blade is got two middle breaks, is respectively b, c, is respectively (Zb, Wb), (Zc, Wc) corresponding to the b of Fa, the coordinate that c is ordered, coordinate expression formula convolution (13), (14):

$\left\{\begin{array}{c}\mathrm{Zb}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+H1,m=1\\ \mathrm{Zb}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+H1,m=2,\·\·\·,n-2\end{array}\right.---\left(15\right)$

Wb＝R×sin(η _m)-K1 (16)

Wherein m=1,2 ... n-2=1,2,

$\left\{\begin{array}{c}\mathrm{Zc}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+S,m=1\\ \mathrm{Zc}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+S,m=2,\·\·\·,n-2\end{array}\right.---\left(17\right)$

Wc＝R×sin(η _m)-K2 (18)

Wherein m=1,2 ... n-2=1,2,

H1, K1, K2, S are empirical value, and value is respectively: H1=40mm, K1=90mm; K2=305mm; S=0mm;

D is vane tip arbitrfary point, is (Zd, Wd) corresponding to the d point coordinate of Fa, coordinate expression formula convolution (13), (14):

$\left\{\begin{array}{c}\mathrm{Zd}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+S-H2,m=1\\ \mathrm{Zd}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+S-H2,m=2,\·\·\·,n-2\end{array}\right.---\left(19\right)$

Wd＝R×sin(η _m)-K3 (20)

Wherein m=1,2 ... n-2,

H2, K3 are empirical value, and value is respectively: H2=80mm, K3=420mm;

Helical blade in base cone section, do not get break, blade is γ with the angle of cylinder diametric(al) line, span is: γ=10-24 °, and these routine γ=21 °, are respectively (Za corresponding to the blade bottom arbitrfary point a of Fa and the coordinate of arbitrfary point, top d, Wa), (Zd, Wd), convolution (10), (12), show that the coordinate expression formula that a is ordered is:

Za＝N ₁+…+N _n-(R-R _2n)×cos(η _n)＝N ₁+…+N ₄-(R-R ₈)×cos(η ₄) (21)

Wa＝R×sin(η _n)＝R×sin(η ₄) (22)

D point is with respect to the height B of a along cylinder axis direction linear change, and its expression formula is

$\left\{\begin{array}{c}B=K3-\frac{K3-K4}{N_4-G}\×(\mathrm{Za}-N_1-N_2-N_3),N_1+N_2+N_3\≤\mathrm{Za}\≤N_1\≤N_2+N_3+N_4-G\\ B=K4-\frac{K4-K5}{G}\×[\mathrm{Za}-(N_1+N_2+N_3+N_4-G)],\mathrm{Za}\≥N_1+N_2+N_3+N_4-G\end{array}\right.---\left(23\right)$

In formula, K4, K5, G are empirical value, and value is respectively: K4=300mm, K5=170mm, G=200mm; Convolution (21), (22), (23), show that the coordinate expression formula that d is ordered is:

Zd＝N ₁+…+N _n-(R-R _2n)×cos(η _n)-B×Tan(γ) (24)

Wd＝R×sin(η _n)-B (25)

In cylinder barrel segment, the trajectory equation of moving some A is identical with formula (9) helix equation, that is:

$y=\frac{k_{n-1}}{P_{n-1}}\×(e^{P_{n-1}\×x}-1)=\frac{k_3}{P_3}\×(e^{P_3\×x}-1)---\left(9\right)$

Taking x as independent variable, y is dependent variable

Wherein the transformational relation of x and Fa is:

$x=\frac{\mathrm{\π}\×D_{n-1}}{360}\×\mathrm{Fa}=\frac{\mathrm{\π}\×D_3}{360}\×\mathrm{Fa}---\left(26\right)$

Cylindrical section cylinder helical blade is positioned at the some a on spiral curve, and corresponding to Fa, the parameter coordinate of Z axis and radial direction is (Za, Wa); Convolution (9), (26), show that the coordinate expression formula that a is ordered is:

Za＝N ₁+…+N _n-2+y＝N ₁+N ₂+y (27)

Wa＝D _n-1/2＝D ₃/2 (28)

Get a break b for cylindrical section cylinder helical blade, the coordinate of ordering corresponding to the b of Fa is respectively (Zb, Wb), its coordinate figure expression formula convolution (27), (28):

Zb＝N ₁+…+N _n-2+y+H1 (29)

Wb＝D _n-1/2-K1 (30)

D is vane tip arbitrfary point, is (Zd, Wd) corresponding to the d point coordinate of Fa, and convolution (27), (28) show that the coordinate expression formula that d is ordered is:

Zd＝N ₁+…+N _n-2+y+S (31)

Wd＝D _n-1/2-K3。(32)

The rotation angle Fa changing method of described blade: in the time determining the 1st section of blade rotary angle Fa to the 3rd section of cylinder, Fa all changes since 0 degree at each section of cylinder tube port position, sets intermediate variable: M ₁, M ₂, recording the 1st section of rotation of each section of cylinder blade screw line to n-2 section cylinder to the rotation angle Fa actual numerical value at the bottom of each section of cylinder cylinder, each section of cylinder blade rotary angle Fa actual numerical value expression formula be, that is: Fa _real:

The 1st section: Fa _real=Fa

The 2nd section: Fa _real=Fa+M ₁

The 3rd section: Fa _real=Fa+M _n-2=Fa+M ₂

Wherein Fa increases since 0 degree according to step-length successively at each section of cylinder, sets change step ii=1 degree, that is: Fa=Fa+ii, until each section of cylinder blade screw line rotation is at the bottom of each section of cylinder cylinder;

Tail cone section cylinder rotation angle Fa changing method:

Because tail cone section cylinder is according to coordinate system direction, be from changing to nozzle at the bottom of cylinder, therefore tail cone section cylinder rotation angle Fa changes to nozzle at the bottom of by cylinder in the time of actual computation.To set Ta be tail cone section cylinder blade change to tin from nozzle at the bottom of the anglec of rotation, to distinguish Fa, Ta increases according to step-length successively from 0 degree, draws rotation angle Ta when blade screw line arrives cylinder bear building-up bundle, is designated as M ₄, therefore, in the time determining Fa, according to the rotation angle M from drawing to nozzle at the bottom of cylinder ₄reduce successively according to step-length, Fa=Fa-ii, until be 0, sets intermediate variable M ₃, record blade screw line and rotate to the rotation angle Fa actual numerical value at the bottom of the last period cylinder cylinder, tail cone section cylinder Fa actual numerical value expression formula is:

N section: Fa _real=M _n-1+ M _n-Fa=M ₃+ M ₄-Fa.

In both sides, described each section of cylindrical shell junction, transition section region is set, the blade arc joint in the each section of cylinder in blade arc two ends, described transition section region and both sides seamlessly transits.

When described cylinder hop count is four sections of cylinders, its method for designing of the 1st section to the 2nd section is: that 1. sets this transition section region is respectively GD1 and GD2 along axial length, as shown in Figure 3; 2. determine horizontal ordinate Za1 and the Za2 of circular section, transition section edge and blade intersection point, Za1=N ₁-GD1, Za2=N ₁+ GD2; 3. the top point d ordinate with respect to Za1 and Za2 is determined in convolution (13), (20), in the 1st section of cylinder, is: $\mathrm{Wd}1=(\frac{\mathrm{Za}1}{\cos {\mathrm{\η}}_1}+R_1)\×\sin {\mathrm{\η}}_1-K_3,$ In the 2nd section of cylinder, be: $\mathrm{Wd}2=(\frac{\mathrm{GD}2}{\cos {\mathrm{\η}}_2}+R_3)\×\sin {\mathrm{\η}}_2-K_3;$ 4. determine the linear rate of change of ordinate of top point d, for show that the top point d ordinate expression formula that transition section changes is: Wd=Wd1+ △ 1[Za-(N ₁-GD1)], the horizontal ordinate that d is ordered calculates according to formula (19); 5. a, b, c point horizontal stroke, ordinate calculate according to formula (13)-(18) in transition section;

The method for designing of the 2nd section to the 3rd section is: that 1. sets this transition section region is respectively GD3 and GD4 along axial length, as shown in Figure 3; 2. determine horizontal ordinate Za3 and the Za4 of circular section, transition section edge and blade intersection point, Za3=N ₁+ N ₂-GD3, Za4=N ₁+ N ₂+ GD4; 3. determine the horizontal ordinate rate of change with respect to the break c of Za3 and Za4: the horizontal ordinate expression formula of the break c that draws variation in transition section: Zc=Za+S+ △ 2 × [Za-(N ₁+ N ₂-GD3)], c point ordinate calculates according to formula (18) in the 2nd section of cylinder, and in the 3rd section of cylinder, expression formula is: Wc=D _n-1/ 2-K2,4. determines the d point horizontal ordinate rate of change with respect to Za3 and Za4, the horizontal ordinate expression formula of the top point d that draws variation in transition section: Zd=Za+S-H2+ △ 3 × [Za-(N ₁+ N ₂-GD3)], and convolution (13), (20), (32) draw the ordinate of d point with respect to Za3 and Za4: in the 2nd section of cylinder, be: $\mathrm{Wd}3=(\frac{N_2-\mathrm{GD}3}{\cos {\mathrm{\η}}_2}+R_3)\×\sin {\mathrm{\η}}_3-K_3,$ In the 3rd section of cylinder, be: $\mathrm{Wd}4=\frac{D_3}{2}-K3;$ Thus, determine the linear rate of change of ordinate of the top point d of transition section variation, for the ordinate expression formula of the top point d that draws variation in transition section: Wd=Wd3+ △ 4[Za-(N ₁+ N ₂-GD3)]; 5. a, b point horizontal stroke, the coordinate figure of ordinate in transition section calculate according to formula (13)-(16) in the 2nd section of cylinder, in the 3rd section of cylinder, calculate according to formula (27)-(30);

The method for designing of the 3rd section to the 4th section is: that 1. sets this transition section region is respectively GD5 and GD6 along axial length, as shown in Figure 3; 2. determine horizontal ordinate Za5 and the Za6 of circular section, transition section edge and blade intersection point, Za5=N ₁+ N ₂+ N ₃-GD5, Za6=N ₁+ N ₂+ N ₃+ GD6; 3. determine the horizontal ordinate rate of change with respect to the break b of Za5 and Za6: the horizontal ordinate expression formula of the break b that draws variation in transition section: Zb=Za+H1+ △ 5 × [Za-(N ₁+ N ₂+ N ₃-GD5)], b point ordinate calculates according to formula (30) in the 3rd section of cylinder, and in the 4th section of cylinder, convolution (22) obtains expression formula: Wb=R × sin (η _n4.)-K1 determines the d point horizontal ordinate rate of change with respect to Za3 and Za4,

the horizontal ordinate expression formula of the top point d that draws variation in transition section: Zd=Za+S-△ 6 × [Za-(N ₁+ N ₂+ N ₃-GD5)], and convolution (21), (23), (25) and (30) draw the ordinate expression formula of d point with respect to Za5 and Za6: in the 3rd section of cylinder, be: in the 4th section of cylinder, be: $\mathrm{Wd}6=(\frac{N_4-\mathrm{GD}6}{\cos {\mathrm{\η}}_4}+R_8)\×\sin {\mathrm{\η}}_4-[K3-\frac{K3-K4}{N_4-G}\×\mathrm{GD}6];$ Thus, determine the linear rate of change of ordinate of the top point d of transition section variation, for the ordinate expression formula of the top point d that draws variation in transition section: Wd=Wd5+ △ 7[Za-(N ₁+ N ₂+ N ₃-GD5)]; 5. a point horizontal stroke, the coordinate figure of ordinate in transition section, calculates according to formula (27), (28) at the 3rd section, calculates according to formula (21), (22) at the 4th section;

In above-mentioned each step: Za draws according to the calculation expression of a point horizontal ordinate on each section of helical blade.

Setting each section of transition section length is respectively: GD1=200mm, GD2=200mm, GD3=200mm, GD4=200mm, GD5=300mm, GD6=200mm;

Described blade is discharge blade and the blade that is connected with feed pipe in the feed pipe punishment of prostomum section, and setting feed pipe mouth of pipe place diameter is Dg1=488mm, and pipe end diameter is Dg2=496.9mm,

Feed pipe length is: $\mathrm{Lg}=\frac{2\×K3-D1+\mathrm{Dg}2}{2\tan {\mathrm{\η}}_1},$

The method for designing of its discharge blade is:

Setting the length of discharge blade in tubular axis direction is Zg=200mm, elemental height is Ko=150mm, stopping height is K3-K2 with the distance of feed pipe outer wall, get 1 break b, on blade, the coordinate expression way of each point a, b, c is respectively a (Za, Wa) point coordinate value is calculated according to formula (13), (14), and b (Zb, Wb) point coordinate expression formula is:

$\mathrm{Zb}=\mathrm{Za}+\frac{H1\×\mathrm{Za}}{\mathrm{Zg}+S}$

$\mathrm{Wb}=\mathrm{Wa}-\frac{K1-\mathrm{Ko}/2}{\mathrm{Zg}+S}\×\mathrm{Za}-\mathrm{Ko}/2$

Blade tip c point with respect to a point height B 1 expression formula is:

$\begin{array}{c}B1=\frac{\mathrm{Za}+\mathrm{Za}/(\mathrm{Zg}+S)\×S}{\mathrm{Zg}}[\frac{D_1-\mathrm{Dg}1}{2}-K3+K2-(\mathrm{Zg}-H2)\frac{\mathrm{Dg}2-\mathrm{Dg}1}{2\mathrm{Lg}}-\mathrm{Ko}]\\ +\mathrm{Za}\tan {\mathrm{\η}}_1+\mathrm{Ko}\end{array}$

C (Zc, Wc) point coordinate expression formula is:

$\mathrm{Zc}=\mathrm{Za}+\frac{\mathrm{Za}}{\mathrm{Zg}+S}\×S$

Wc＝Wa-B1

Its blade design method that is connected with feed pipe is:

Its length L of blade that is connected with feed pipe is L=Lg-Zg, on blade, get two break b, c, on blade, the coordinate expression way of each point a, b, c, d is respectively: a (Za, Wa) point, b (Zb, Wb) point coordinate value is calculated according to formula (13), (14), (15), (16)

C (Zc, Wc) point coordinate expression formula is:

Zc＝Za+S

Wc＝Wa-B2+K3-K2

Blade tip d point with respect to a point height B 2 expression formulas is:

$B2=\frac{D_1-\mathrm{Dg}1}{2}+\mathrm{Za}\×\tan {\mathrm{\η}}_1-[\mathrm{Za}-(H2+S)]\×\frac{\mathrm{Dg}2-\mathrm{Dg}1}{2\mathrm{Lg}}$

D (Zd, Wd) point coordinate expression formula is:

Zd＝Za+S-H2

Wd＝Wd-B2。

The helical blade that helical blade method for designing according to the present invention obtains, is two at churn internal helical blades, interlaced 180 ° of arrangements.

Embodiment 3: this example as different from Example 2: when described cylinder is three sections of cylinders, transition section is determined transition section region according to the method for designing of the 2nd section to the 3rd section and the 3rd section to the 4th section described in embodiment 2.Wherein each parameter is: H1=20mm, K1=70mm; K2=280mm; S=10mm; H2=60mm, K3=400mm; γ=18 °, K4=280mm, K5=150mm, G=180mm; Described change step ii=10 degree.Each section of transition section length is respectively: GD1=200mm, GD2=200mm, GD3=200mm, GD4=200mm.Dg1＝470mm，Dg2＝480mm，Zg＝185mm，Ko＝145mm。

Embodiment 4: this example as different from Example 2: each parameter is: H1=80mm, K1=120mm; K2=350mm; S=30mm; H2=100mm, K3=440mm; γ=24 ° K4=320mm, K5=200mm, G=240mm; Described change step ii=20 degree.Each section of transition section length is respectively: GD1=200mm, GD2=200mm, GD3=200mm, GD4=200mm, GD5=300mm, GD6=200mm; Dg1=500mm, Dg2=510mm, Zg=210mm, Ko=160mm.

Claims (9)

1. the method for designing based on linear change helix angle concrete stirring vane, is characterized in that: blade changes at the bottom of from nozzle to cylinder continuously, comprises the steps:

The first step: according to plane isogonism log spiral R=R ₀× e ^{k θ}, according to its character k=cot β, the relational expression drawing:

R'/R＝k＝cotβ (1)

Wherein, R is utmost point footpath, and θ is polar angle, R ₀for initial utmost point footpath, set R ₀=1, k is constant, and β is helix angle, and R' represents that R is to θ differentiate, and e is mathematics Euler's constant, is the truth of a matter of natural logarithm function;

Second step: by changing its K value, its span is 0.25～0.36 according to formula (1), to change helixangleβ, setting cone section cylinder nozzle is minor diameter place, and the cylinder end is major diameter place, and the k value of establishing each section of cylinder nozzle and cylinder bottom is k _j, j=1,2,3 ... n+1, the hop count that n is churn, n>=3 and n are integer, setting the initial k value of nozzle cone section blade is k ₁, cylinder base cone section blade finishes k value for k _n+1, and k _n+1> k ₁, make k ₁with k _n+1along cylinder axis direction linear change, the interconversion rate PP that obtains k value edge cylinder axis direction is:

$\mathrm{PP}=\frac{k_{n+1}-k_1}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i}---\left(2\right)$

Wherein N _i, i=1,2 ... n, represents each section of cylinder axis direction length;

Determine that according to formula (2) each section of cylinder is at the k of junction value k _j, that is: j=2,3 ... n:

$k_j=k_1+\mathrm{pp}\×\left(\underset{i=1}{\overset{j-1}{\mathrm{\Σ}}}{N}_i\right)---\left(3\right)$

The 3rd step: set D _lfor the diameter of churn nozzle, the cylinder end and each section of cylinder junction, l=1,2 ... n+1; Set inner cone section R _2m-1for utmost point footpath corresponding to nozzle, inner cone section R _2mfor utmost point footpath corresponding at the bottom of cylinder; Base cone section R _2n-1for utmost point footpath corresponding at the bottom of cylinder, base cone section R _2nfor utmost point footpath corresponding to nozzle, make the k value of each cone section cylinder along utmost point footpath R direction linear change, obtain each cone section cylinder k value rate of change P _m:

$P_m=\frac{k_{m+1}-k_m}{R_{2m}-R_{2m-1}},m=\mathrm{1,2}\·\·\·n,m\≠n-1---\left(4\right)$

In formula: inner cone section: $R_{2m-1}=\frac{D_m}{2\sin {\mathrm{\η}}_m},R_{2m}=\frac{D_{m+1}}{2\sin {\mathrm{\η}}_m},$

Base cone section: $R_{2n-1}=\frac{D_n}{2\sin {\mathrm{\η}}_n},R_{2n}=\frac{D_{n+1}}{2\sin {\mathrm{\η}}_n},$

η _mfor the circular cone element line angle of each cone section, m=1,2 ... n, m ≠ n-1,

Obtain the conical section helix differential equation according to formula (1) and formula (4):

$\frac{R^{\′}}{R}=k_m+P_m\×(R-R_{2m-1})---\left(5\right)$

K _mrepresent the initial k value of each cone section cylinder, that is: m=1,2 ... n, m ≠ n-1;

Cylindrical section cylinder blade curve adopts variable slope curve to replace log spiral, and the slope using the k value of cylindrical section cylinder as developed curve, makes k value linear change vertically; Obtain

Cylindrical section cylinder k value rate of change: $P_{n-1}=\frac{k_n-k_{n-1}}{N_{n-1}}---\left(6\right)$

Obtain the cylindrical section helix differential equation according to the funtcional relationship of formula (6) and rate of curve:

$\frac{\mathrm{dy}}{\mathrm{dx}}=k_{n-1}+P_{n-1}y---\left(7\right)$

The 4th step: the helix equation that is obtained each cone section cylinder by formula (5) is:

$\frac{R}{R+k_m/P_m-R_{2m-1}}=\frac{P_m\×R_{2m-1}}{k_m}\×e^{\left({\mathrm{\θ}-\mathrm{\θ}}_m\right)\×(k_m-P_m\×R_{2m-1})}---\left(8\right)$

By formula R=R ₀× e ^{k θ}, R ₀=1, obtain in formula m=1,2 ... n, m ≠ n-1;

The helix equation that is drawn cylindrical section cylinder by formula (6), (7) is:

$y=\frac{k_{n-1}}{P_{n-1}}\×(e^{P_{n-1}\×x}-1)---\left(9\right)$

Wherein x, y are plane coordinate system direction, and x is along cylindrical drum diametric(al), and y is cylindrical drum axis direction, and x is independent variable, and y is dependent variable.

2. the method for designing based on linear change helix angle concrete stirring vane according to claim 1, it is characterized in that: when described each section of blade shape is different, according to the respectively helix equation of the section of cone cylinder and cylindrical section cylinder of blade, calculate the coordinate of blade each point:

Taking the nozzle center of circle of churn as true origin, taking the central axis of churn as Z axis, and with feedstock direction for just, adopt cylindrical-coordinate system taking Z axis as dead axle line, the coordinate of radial direction represents with W, and rotation angle represents with Fa, taking degree as unit, and press left hand helix direction rotation

The parameter expression mode of helical blade under this coordinate system is: be selected in a moving some A on barrel, the spiral curve of blade is drawn in this variation with helical blade rotation angle Fa on barrel,

According to formula (8), taking θ as independent variable, R is dependent variable, and conversion obtains the trajectory equation of moving some A on cone section cylinder and is:

$R=\frac{(\frac{k_m}{P_m}-R_{2m-1})\×\frac{P_m\×R_{2m-1}}{k_m}\×e^{(\mathrm{\θ}-{\mathrm{\θ}}_m)\×(k_m-P_m\×R_{2m-1})}}{1-\frac{P_m\×R_{2m-1}}{k_m}\×e^{(\mathrm{\θ}-{\mathrm{\θ}}_m)\×(k_m-P_m\×R_{2m-1})}}---\left(10\right)$

Wherein: m=1,2 ... n, m ≠ n-1,

In formula, θ is the corresponding polar angle of curve while launching along cylindrical shell, and unit is radian, and the transformational relation of it and rotation angle Fa is:

$\frac{\mathrm{\θ}-{\mathrm{\θ}}_m}{D_m/R_{2m-1}\×180}\×\frac{180}{\mathrm{\π}}=\frac{\mathrm{Fa}}{360},---\left(11\right)$

Wherein m=1,2 ... n, m ≠ n-1,

Abbreviation obtains:

$\mathrm{\θ}=\frac{\mathrm{Fa}\×D_m\×\mathrm{\π}}{R_{2m-1}\×360}+{\mathrm{\θ}}_m---\left(12\right)$

Be positioned at the some a on spiral curve for inner cone section helical blade, corresponding to Fa, the parameter coordinate of its Z axis and radial direction is (Za, Wa); According to formula (10), (12), show that the coordinate expression formula that on blade, a is ordered is:

$\left\{\begin{array}{c}\mathrm{Za}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right),m=1\\ \mathrm{Za}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1},m=2,\·\·\·,n-2\end{array}\right.---\left(13\right)$

Wa＝R×sin(η _m) (14)

Wherein m=1,2 ... n-2,

Get two middle breaks for inner cone end blade, be respectively b, c, be respectively (Zb, Wb), (Zc, Wc) corresponding to the b of Fa, the coordinate that c is ordered, coordinate expression formula convolution (13), (14):

$\left\{\begin{array}{c}\mathrm{Zb}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+H1,m=1\\ \mathrm{Zb}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+H1,m=2,\·\·\·,n-2\end{array}\right.---\left(15\right)$

Wb＝R×sin(η _m)-K1 (16)

Wherein m=1,2 ... n-2,

$\left\{\begin{array}{c}\mathrm{Zc}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+S,m=1\\ \mathrm{Zc}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+S,m=2,\·\·\·,n-2\end{array}\right.---\left(17\right)$

Wc＝R×sin(η _m)-K2 (18)

Wherein m=1,2 ... n-2,

H1, K1, K2, S are empirical value, and span is respectively: H1=20-80mm, K1=70-120mm; K2=280-350mm; S=0-30mm;

D is vane tip arbitrfary point, is (Zd, Wd) corresponding to the d point coordinate of Fa, coordinate expression formula convolution (13), (14):

$\left\{\begin{array}{c}\mathrm{Zd}=(R-R_1)\×\cos \left({\mathrm{\η}}_1\right)+S-H2,m=1\\ \mathrm{Zd}=(R-R_{2m-1})\×\cos \left({\mathrm{\η}}_m\right)+N_1+\·\·\·+N_{m-1}+S-H2,m=2,\·\·\·,n-2\end{array}\right.---\left(19\right)$

Wd＝R×sin(η _m)-K3 (20)

Wherein m=1,2 ... n-2,

H2, K3 are empirical value, and span is respectively: H2=60-100mm, K3=400-440mm;

Helical blade in base cone section, do not get break, blade is γ with the angle of cylinder diametric(al) line, span is: γ=10-24 °, be respectively (Za, Wa), (Zd, Wd) corresponding to the blade bottom arbitrfary point a of Fa and the coordinate of arbitrfary point, top d, convolution (10), (12), show that the coordinate expression formula that a is ordered is:

Za＝N ₁+…+N _n-(R-R _2n)×cos(η _n) (21)

Wa＝R×sin(η _n) (22)

D point is with respect to the height B of a along cylinder axis direction linear change, and its expression formula is

$\left\{\begin{array}{c}B=K3-\frac{K3-K4}{N_4-G}\×(\mathrm{Za}-N_1-N_2-N_3),N_1+N_2+N_3\≤\mathrm{Za}\≤N_1\≤N_2+N_3+N_4-G\\ B=K4-\frac{K4-K5}{G}\×[\mathrm{Za}-(N_1+N_2+N_3+N_4-G)],\mathrm{Za}\≥N_1+N_2+N_3+N_4-G\end{array}\right.---\left(23\right)$

In formula, K4, K5, G are empirical value, and span is respectively: K4=280-320mm, K5=150-200mm, G=180-240mm; Convolution (21), (22), (23), show that the coordinate expression formula that d is ordered is:

Zd＝N ₁+…+N _n-(R-R _2n)×cos(η _n)-B×Tan(γ) (24)

Wd＝R×sin(η _n)-B (25)

In cylinder barrel segment, the trajectory equation of moving some A is identical with formula (9) helix equation, that is:

$y=\frac{k_{n-1}}{P_{n-1}}\×(e^{P_{n-1}\×x}-1)---\left(9\right)$

Taking x as independent variable, y is dependent variable

Wherein the transformational relation of x and Fa is:

$X=\frac{\mathrm{\π}\×D_{n-1}}{360}\×\mathrm{Fa}---\left(26\right)$

Cylindrical section cylinder helical blade is positioned at the some a on spiral curve, and corresponding to Fa, the parameter coordinate of Z axis and radial direction is (Za, Wa); Convolution (9), (26), show that the coordinate expression formula that a is ordered is:

Za＝N ₁+…+N _n-2+y (27)

Wa＝D _n-1/2 (28)

Get a break b for cylindrical section cylinder helical blade, the coordinate of ordering corresponding to the b of Fa is respectively (Zb, Wb), its coordinate figure expression formula convolution (27), (28):

Zb＝N ₁+…+N _n-2+y+H1 (29)

Wb＝D _n-1/2-K1 (30)

D is vane tip arbitrfary point, is (Zd, Wd) corresponding to the d point coordinate of Fa, and convolution (27), (28) show that the coordinate expression formula that d is ordered is:

Zd＝N ₁+…+N _n-2+y+S (31)

Wd＝D _n-1/2-K3。(32)

3. the method for designing based on linear change helix angle concrete stirring vane according to claim 1, it is characterized in that: the rotation angle Fa changing method of described blade: in the time determining the 1st section of blade rotary angle Fa to n-1 section cylinder, Fa all since 0 ° of variation, sets intermediate variable: M at each section of cylinder tube port position ₁, M ₂..., M _n-2, recording the rotation of each section of cylinder blade screw line to the rotation angle Fa actual numerical value at the bottom of each section of cylinder cylinder, each section of cylinder blade rotary angle Fa actual numerical value expression formula be, that is: Fa _real:

The 1st section: Fa _real=Fa

The 2nd section: Fa _real=Fa+M ₁

………

N-1 section: Fa _real=Fa+M _n-2

Wherein Fa increases since 0 according to step-length successively at each section of cylinder, sets change step ii, that is: Fa=Fa+ii, until each section of cylinder blade screw line rotation is at the bottom of each section of cylinder cylinder;

Tail cone section cylinder, i.e. n section cylinder, rotation angle Fa changing method:

The anglec of rotation that to set Ta be tail cone section cylinder blade at the bottom of changing to tin from nozzle, Ta increases according to step-length successively from 0, draws rotation angle Ta when blade screw line arrives cylinder bear building-up bundle, is designated as M _n, in the time determining Fa, according to the rotation angle M drawing _n, the Fa making is from reducing successively according to step-length to nozzle at the bottom of cylinder, and Fa=Fa-ii, until be 0, sets intermediate variable M _n-1, record blade screw line and rotate to the rotation angle Fa actual numerical value at the bottom of the last period cylinder cylinder, tail cone section cylinder Fa actual numerical value expression formula is:

N section: Fa _real=M _n-1+ M _n-Fa.

4. the method for designing based on linear change helix angle concrete stirring vane according to claim 3, is characterized in that: described change step ii is greater than 0 degree and is less than or equal to 20 degree.

5. the method for designing based on linear change helix angle concrete stirring vane according to claim 2, it is characterized in that: in both sides, described each section of cylindrical shell junction, transition section region is set, the blade arc joint in the each section of cylinder in blade arc two ends, described transition section region and both sides seamlessly transits.

6. the method for designing based on linear change helix angle concrete stirring vane according to claim 5, it is characterized in that: when described cylinder hop count is four sections of cylinders, its method for designing of the 1st section to the 2nd section is: that 1. sets this transition section region is respectively GD1 and GD2 along axial length; 2. determine horizontal ordinate Za1 and the Za2 of circular section, transition section edge and blade intersection point, Za1=N ₁-GD1, Za2=N ₁+ GD2; 3. the top point d ordinate with respect to Za1 and Za2 is determined in convolution (13), (20), in the 1st section of cylinder, is: $\mathrm{Wd}1=(\frac{\mathrm{Za}1}{\cos {\mathrm{\η}}_1}+R_1)\×\sin {\mathrm{\η}}_1-K_3,$ In the 2nd section of cylinder, be: $\mathrm{Wd}2=(\frac{\mathrm{GD}2}{\cos {\mathrm{\η}}_2}+R_3)\×\sin {\mathrm{\η}}_2-K_3;$ 4. determine the linear rate of change of ordinate of top point d, for show that the top point d ordinate expression formula that transition section changes is: Wd=Wd1+ △ 1[Za-(N ₁-GD1)], the horizontal ordinate that d is ordered calculates according to formula (19); 5. a, b, c point horizontal stroke, ordinate calculate according to formula (13)-(18) in transition section;

The method for designing of the 2nd section to the 3rd section is: that 1. sets this transition section region is respectively GD3 and GD4 along axial length; 2. determine horizontal ordinate Za3 and the Za4 of circular section, transition section edge and blade intersection point, Za3=N ₁+ N ₂-GD3, Za4=N ₁+ N ₂+ GD4; 3. determine the horizontal ordinate rate of change with respect to the break c of Za3 and Za4: the horizontal ordinate expression formula of the break c that draws variation in transition section: Zc=Za+S+ △ 2 × [Za-(N ₁+ N ₂-GD3)], c point ordinate calculates according to formula (18) in the 2nd section of cylinder, and in the 3rd section of cylinder, expression formula is: Wc=D _n-1/ 2-K2,4. determines the d point horizontal ordinate rate of change with respect to Za3 and Za4, the horizontal ordinate expression formula of the top point d that draws variation in transition section: Zd=Za+S-H2+ △ 3 × [Za-(N ₁+ N ₂-GD3)], and convolution (13), (20), (32) draw the ordinate of d point with respect to Za3 and Za4: in the 2nd section of cylinder, be: $\mathrm{Wd}3=(\frac{N_2-\mathrm{GD}3}{\cos {\mathrm{\η}}_2}+R_3)\×\sin {\mathrm{\η}}_3-K_3,$ In the 3rd section of cylinder, be: $\mathrm{Wd}4=\frac{D_{n-1}}{2}-K3;$ Thus, determine the linear rate of change of ordinate of the top point d of transition section variation, for the ordinate expression formula of the top point d that draws variation in transition section: Wd=Wd3+ △ 4[Za-(N ₁+ N ₂-GD3)]; 5. a, b point horizontal stroke, the coordinate figure of ordinate in transition section calculate according to formula (13)-(16) in the 2nd section of cylinder, in the 3rd section of cylinder, calculate according to formula (27)-(30);

The method for designing of the 3rd section to the 4th section is: that 1. sets this transition section region is respectively GD5 and GD6 along axial length; 2. determine horizontal ordinate Za5 and the Za6 of circular section, transition section edge and blade intersection point, Za5=N ₁+ N ₂+ N ₃-GD5, Za6=N ₁+ N ₂+ N ₃+ GD6; 3. determine the horizontal ordinate rate of change with respect to the break b of Za5 and Za6: the horizontal ordinate expression formula of the break b that draws variation in transition section: Zb=Za+H1+ △ 5 × [Za-(N ₁+ N ₂+ N ₃-GD5)], b point ordinate calculates according to formula (30) in the 3rd section of cylinder, and in the 4th section of cylinder, convolution (22) obtains expression formula: Wb=R × sin (η _n)-K1

4. determine the d point horizontal ordinate rate of change with respect to Za5 and Za6, the horizontal ordinate expression formula of the top point d that draws variation in transition section: Zd=Za+S-△ 6 × [Za-(N ₁+ N ₂+ N ₃-GD5)], and convolution (21), (23), (25) and (30) draw the ordinate of d point with respect to Za5 and Za6: in the 3rd section of cylinder, be:

in the 4th section of cylinder, be:

$\mathrm{Wd}6=(\frac{N_4-\mathrm{GD}6}{\cos {\mathrm{\η}}_4}+R_8)\×\sin {\mathrm{\η}}_4-[K3-\frac{K3-K4}{N_4-G}\×\mathrm{GD}6];$ Thus, determine the linear rate of change of ordinate of the top point d of transition section variation, the ordinate expression formula of the top point d that draws variation in transition section: Wd=Wd5+ △ 7[Za-(N ₁+ N ₂+ N ₃-GD5)]; 5. a point horizontal stroke, the coordinate figure of ordinate in transition section, calculates according to formula (27), (28) at the 3rd section, calculates according to formula (21), (22) at the 4th section;

In above-mentioned each step: Za draws according to the calculation expression of a point horizontal ordinate on each section of helical blade.

7. the method for designing based on linear change helix angle concrete stirring vane according to claim 5, it is characterized in that: when described cylinder is three sections of cylinders, determine transition section region according to the method for designing of the 2nd section to the 3rd section and the 3rd section to the 4th section described in claim 5.

8. the method for designing based on linear change helix angle concrete stirring vane according to claim 2, it is characterized in that: described blade is discharge blade and the blade that is connected with feed pipe in the feed pipe punishment of prostomum section, setting feed pipe mouth of pipe place diameter is Dg1=470-500mm, pipe end diameter is Dg2=480-510mm, and feed pipe length L g is:

The method for designing of its discharge blade is:

Setting the length of discharge blade in tubular axis direction is Zg, Zg=170-210mm, elemental height is Ko, Ko=140-160mm, stopping height is K3-K2 with the distance of feed pipe outer wall, gets 1 break b, on blade, the coordinate expression way of each point a, b, c is respectively: a (Za, Wa) point coordinate value is calculated according to formula (13), (14), and b (Zb, Wb) point coordinate expression formula is:

$\mathrm{Zb}=\mathrm{Za}+\frac{H1\×\mathrm{Za}}{\mathrm{Zg}+S}$

$\mathrm{Wb}=\mathrm{Wa}-\frac{K1-\mathrm{Ko}/2}{\mathrm{Zg}+S}\×\mathrm{Za}-\mathrm{Ko}/2$

Blade tip c point with respect to a point height B 1 expression formula is:

$\begin{array}{c}B1=\frac{\mathrm{Za}+\mathrm{Za}/(\mathrm{Zg}+S)\×S}{\mathrm{Zg}}[\frac{D_1-\mathrm{Dg}1}{2}-K3+K2-(\mathrm{Zg}-H2)\frac{\mathrm{Dg}2-\mathrm{Dg}1}{2\mathrm{Lg}}-\mathrm{Ko}]\\ +\mathrm{Za}\tan {\mathrm{\η}}_1+\mathrm{Ko}\end{array}$

C (Zc, Wc) point coordinate expression formula is:

$\mathrm{Zc}=\mathrm{Za}+\frac{\mathrm{Za}}{\mathrm{Zg}+S}\×S$

Wc＝Wa-B1

The blade design method that is connected with feed pipe is:

Its length L of blade that is connected with feed pipe is: L=Lg-Zg, on blade, get two break b, c, on blade, the coordinate expression way of each point a, b, c, d is respectively: a (Za, Wa) point, b (Zb, Wb) point coordinate value is calculated according to formula (13), (14), (15), (16)

C (Zc, Wc) point coordinate expression formula is:

Zc＝Za+S

Wc＝Wa-B2+K3-K2

Blade tip d point with respect to a point height B 2 expression formulas is:

$B2=\frac{D_1-\mathrm{Dg}1}{2}+\mathrm{Za}\×\tan {\mathrm{\η}}_1-[\mathrm{Za}-(H2+S)]\×\frac{\mathrm{Dg}2-\mathrm{Dg}1}{2\mathrm{Lg}}$

D (Zd, Wd) point coordinate expression formula is:

Zd＝Za+S-H2

Wd＝Wa-B2。

9. the method for designing based on linear change helix angle concrete stirring vane according to claim 6, is characterized in that: described GD1～GD6 span is respectively 150-400mm.