CN104182574B - Design method based on linear change helical angle concrete stirring vane - Google Patents

Design method based on linear change helical angle concrete stirring vane Download PDF

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CN104182574B
CN104182574B CN201410405986.0A CN201410405986A CN104182574B CN 104182574 B CN104182574 B CN 104182574B CN 201410405986 A CN201410405986 A CN 201410405986A CN 104182574 B CN104182574 B CN 104182574B
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mrow
msub
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cylinder
blade
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CN104182574A (en
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李斌
王凯威
刘杰
肖凡
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Shenyang Jianzhu University
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Shenyang Jianzhu University
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Abstract

The invention discloses a kind of design method based on linear change helical angle concrete stirring vane, belong to building machinery design field.The spiral blade designed using the inventive method, with good fitting performance, the performance requirement of blade stirring and discharging can be taken into account, and cause the linear variation relation of helical angle of different cylinder section inside spin stirring vanes, so that the helix in different cylinder sections is formed in cylinder junction and seamlessly transitted, the continuity of helix ensure that.The helical angle and blade shape of its blade can realize the consecutive variations from nozzle to cylinder bottom according to each section of cylinder function.Also concrete can be effectively prevented to bond in such position, the task performance of concrete mixer truck can be effectively improved.

Description

Design method based on linear change helical angle concrete stirring vane
Technical field
The invention belongs to building machinery design field, it is related to a kind of based on linear change helical angle concrete stirring vane Design method.
Background technology
For the design method of concrete mixer truck helical blade, a kind of is the concept for being introduced in conical section calculating cone, is counted Calculate and use log spiral on cone, be then with reference to the helix that cylinder inboard wall is calculated to calculate cone, it is indicated that cylinder inboard wall The change linear approximate relationship of helix helical angle；But because this method does not point out the number of non-equiangular logarithm helical curve Rule is learned, is implemented more complicated.The research having in addition is thought, when the helixangleβ in log spiral expression formula is constant When, the expression formula is log spiral, and when helixangleβ is a variable, the expression formula is non-equiangular logarithm helical curve；It is but logical Checking is crossed it is recognised that after helixangleβ is that β is expressed as spiral corner Fa function by variable, β can not be by given letter Number relationship change, that is, helixangleβ are uncontrollable, i.e., after the starting point helical angle of helix determines, cannot be pre-designed Terminal helix angle.
The content of the invention
In view of the deficienciess of the prior art, the present invention, which provides one kind, is based on linear change helical angle concrete stirring vane Design method, it can take into account blade stirring and discharging performance requirement, ensure that the continuity of helix.
To achieve the above object, technical scheme is as follows：
A kind of design method based on linear change helical angle concrete stirring vane of the present invention, blade is from nozzle to cylinder bottom Consecutive variations, comprise the following steps：
The first step：According to plane isogonism log spiral R=R0×ekθ, according to its property k=cot β, the relation drawn Formula：
R'/R=k=cot β (1)
Wherein, R is polar diameter, and θ is polar angle, R0To originate polar diameter, R is set0=1, k are constant, and β is helical angle, and R' represents R To θ derivations, e is mathematics Euler's constant, is the truth of a matter of natural logrithm function；
Second step：According to formula (1) by changing its K value, its span is 0.25~0.36, to change helixangleβ, if Fixed cone section cylinder nozzle is at minor diameter, and cylinder bottom is at major diameter, if the k values of each section of cylinder nozzle and cylinder bottom are kj, j=1,2, 3 ... n+1, n are the hop count of mixing drum, and n >=3 and n be integer, it is k that setting nozzle cone section blade, which originates k values,1, cylinder base cone section blade It is k to terminate k valuesn+1, and kn+1＞ k1, make k1With kn+1Along cylinder axis direction linear change, conversion of the k values along cylinder axis direction is obtained Rate PP is：
Wherein Ni, i=1,2 ... n, represent each section of cylinder axis direction length；
K value k of each section of cylinder in junction is determined according to formula (2)j, i.e.,：J=2,3 ... n：
3rd step：Set DlFor the diameter of mixing drum nozzle, cylinder bottom and each section of cylinder junction, l=1,2 ... n+1；Before setting Bore section R2m-1For polar diameter corresponding to nozzle, inner cone section R2mFor polar diameter corresponding to cylinder bottom；Base cone section R2n-1For polar diameter corresponding to cylinder bottom, Base cone section R2nFor polar diameter corresponding to nozzle, make the k values of each cone section cylinder change along polar diameter R dimension linears, obtain each cone section cylinder k values and become Rate Pm：
In formula：Inner cone section：
Base cone section：
ηmFor it is each cone section circular cone element line angle, m=1,2 ... n, m ≠ n-1,
The circular cone section spiral line differential equation is obtained according to formula (1) and formula (4)：
kmEach cone section cylinder starting k values are represented, i.e.,：M=1,2 ... n, m ≠ n-1；
Cylindrical section cylinder blade curve replaces log spiral using variable slope curve, using the k values of cylindrical section cylinder as exhibition The slope of open curve, make k values linear change vertically；Obtain
Cylindrical section cylinder k value changes rates：
The cylinder section spiral line differential equation is obtained according to the functional relation of formula (6) and the slope of curve：
4th step：Obtaining each helix equation for boring section cylinder by formula (5) is：
By formula R=R0×ekθ, R0=1, obtain in formulaM=1,2 ... n, m ≠ n-1；
Show that the helix equation of cylindrical section cylinder is by formula (6), (7)：
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 from change Amount, y is dependent variable.
Further, during each section of blade shape difference, the helix side of section cylinder and cylindrical section cylinder is respectively bored according to blade Journey, the coordinate of blade each point is calculated:
Using the nozzle center of circle of mixing drum as the origin of coordinates, using the central axis of mixing drum as Z axis, and using feedstock direction as Just, the cylindrical-coordinate system using Z axis as dead axle line is used, the coordinate of radial direction represents that the anglec of rotation is represented with Fa with W, is with degree Unit, and rotated by left hand helix direction,
Parameter expression mode of the helical blade under this coordinate system be：A dynamic point A on barrel is selected in, the point is with helical-blade The helical curve of blade is drawn in piece anglec of rotation Fa change on barrel,
According to formula (8), using θ as independent variable, R is dependent variable, and conversion obtains trajectory equations of the dynamic point A on cone section cylinder For：
Wherein：M=1,2 ... n, m ≠ n-1,
In formula θ be curve along cylinder deploy when corresponding polar angle, unit is radian, and its conversion with anglec of rotation Fa is closed It is to be：
Wherein m=1,2 ... n, m ≠ n-1,
Abbreviation obtains：
The point a being located at for inner cone section helical blade on helical curve, corresponding to Fa, the parameter of its Z axis and radial direction Coordinate is (Za, Wa)；According to formula (10), (12), the coordinate expressions for drawing a points on blade are：
Wa=R × sin (ηm) (14)
Wherein m=1,2 ... n-2,
Take two middle breaks, respectively b, c for preceding tapered end blade, corresponding to Fa b, c point coordinate be respectively (Zb, Wb), (Zc, Wc), coordinate expressions convolution (13), (14) obtain：
Wb=R × sin (ηm)-K1 (16)
Wherein m=1,2 ... n-2,
Wc=R × sin (ηm)-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, and the d point coordinates corresponding to Fa is (Zd, Wd), coordinate expressions convolution (13), (14)：
Wd=R × sin (ηm)-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, break is not taken, the angle of blade and cylinder diametric(al) line is γ, and span is： γ=10-24 °, coordinate respectively (Za, Wa), (Zd, the Wd) of blade bottom arbitrfary point a and top arbitrfary point d corresponding to Fa, Convolution (10), (12), the coordinate expressions for drawing a points are：
Za=N1+…+Nn-(R-R2n)×cos(ηn) (21)
Wa=R × sin (ηn)(22)
D points are along cylinder axis direction linear change, its expression formula relative to a height B
K4, K5, G are empirical value in formula, and span is respectively：K4=280-320mm, K5=150-200mm, G= 180-240mm；Then convolution (21), (22), (23), the coordinate expressions for drawing d points are：
Zd=N1+…+Nn-(R-R2n)×cos(ηn)-B×Tan(γ) (24)
Wd=R × sin (ηn)-B (25)
Dynamic point A trajectory equation is identical with formula (9) helix equation in cylinder barrel segment, i.e.,：
Using x as independent variable, y is dependent variable
Wherein x and Fa transformational relation is：
Cylindrical section cylinder helical blade is located at the point a on helical curve, corresponding to Fa, the parameter coordinate of Z axis and radial direction For (Za, Wa)；Convolution (9), (26), the coordinate expressions for drawing a points are：
Za=N1+…+Nn-2+y (27)
Wa=Dn-1/2 (28)
A break b is taken for cylindrical section cylinder helical blade, the coordinate corresponding to Fa b points is respectively (Zb, Wb), and it is sat Scale value expression formula convolution (27), (28) obtain：
Zb=N1+…+Nn-2+y+H1 (29)
Wb=Dn-1/2-K1 (30)
D is vane tip arbitrfary point, and the d point coordinates corresponding to Fa is (Zd, Wd), convolution (27), (28), draws d points Coordinate expressions be：
Zd=N1+…+Nn-2+y+S (31)
Wd=Dn-1/2-K3。 (32)
Further, the anglec of rotation Fa changing methods of the blade：It is determined that the blade rotation of the 1st section to (n-1)th section cylinder During the Fa of angle, Fa changes in each section of cylinder tube port position since 0 °, sets intermediate variable：M1, M2..., Mn-2, record each section of cylinder blade Helix is rotated to the anglec of rotation Fa actual numerical values at each section of cylinder cylinder bottom, each section of cylinder blade anglec of rotation Fa actual numerical value expression formula, I.e.：FaIt is real：
1st section：FaIt is real=Fa
2nd section：FaIt is real=Fa+M1
………
(n-1)th section：FaIt is real=Fa+Mn-2
Wherein Fa increases since 0 successively in each section of cylinder according to step-length, sets change step ii, i.e.,：Fa=Fa+ii, directly Rotated to each section of cylinder blade screw line to each section of cylinder cylinder bottom；
Tail cone section cylinder, i.e. n-th section of cylinder, anglec of rotation Fa changing methods：
The anglec of rotation that Ta changes to a bottom as tail cone section cylinder blade from nozzle is set, Ta increases successively from 0 according to step-length, The anglec of rotation Ta at the end of blade screw line arrival cylinder bottom is drawn, is designated as Mn, it is determined that during Fa, according to the anglec of rotation M drawnn, make Fa reduced successively according to step-length from cylinder bottom to nozzle, Fa=Fa-ii, until for 0, setting intermediate variable Mn-1, record blade spiral shell Spin line is rotated to the anglec of rotation Fa actual numerical values at the last period cylinder cylinder bottom, then tail cone section cylinder Fa actual numerical value expression formulas are：
N-th section：FaIt is real=Mn-1+Mn-Fa。
Further, the change step ii is more than 0 degree and is less than or equal to 20 degree.
Further, changeover portion region, the changeover portion region blade arc are set in each section of cylinder junction both sides Shape both ends seamlessly transit with the blade arc joint in the cylinder of each section of both sides.
Further, when the cylinder hop count is four sections of cylinders, its 1st section to the 2nd section design method is：1. set the changeover portion Region is respectively GD1 and GD2 along axial length,；2. determine changeover portion edge circular section and blade intersection point abscissa Za1 and Za2, Za1=N1- GD1, Za2=N1+GD2；3. convolution (13), (20) determine the top end point d ordinates relative to Za1 and Za2, It is in 1st section of cylinder：It is in 2nd section of cylinder：④ Top end point d ordinate linear change rate is determined, isDraw the top end point d ordinates of changeover portion change Expression formula is：[Za- (the N of Wd=Wd1+ △ 11- GD1)], the abscissa of d points calculates according to formula (19)；5. a, b, c point are horizontal, indulge and sit It is marked in changeover portion and is calculated according to formula (13)-(18)；
2nd section to the 3rd section of design method is：1. set the changeover portion region along axial length be respectively GD3 and GD4；2. determine changeover portion edge circular section and the abscissa Za3 and Za4, Za3=N of blade intersection point1+N2- GD3, Za4=N1+N2 +GD4；3. determine the abscissa rate of change of the break c relative to Za3 and Za4：Draw Abscissa expression formulas of the break c of change in changeover portion：Zc=Za+S+ △ 2 × [Za- (N1+N2- GD3)], c point ordinates exist Calculated in 2nd section of cylinder according to formula (18), expression formula is in the 3rd section of cylinder：Wc=Dn-1/ 2-K2,4. determine relative to Za3 and Za4 D point abscissa rates of change,Draw abscissa expression formulas of the top end point d of change in changeover portion：Zd =Za+S-H2+ △ 3 × [Za- (N1+N2- GD3)], and convolution (13), (20), (32) draw d points relative to Za3's and Za4 Ordinate：It is in the 2nd section of cylinder：It is in the 3rd section of cylinder： Thus, the top end point d of changeover portion change ordinate linear change rate is determined, isDraw the top of change Ordinate expression formulas of the end points d in changeover portion：[Za- (the N of Wd=Wd3+ △ 41+N2-GD3)]；5. a, b points horizontal stroke, ordinate are in mistake The coordinate value crossed in section, calculate according to formula (13)-(16) in the 2nd section of cylinder, calculated in the 3rd section of cylinder according to formula (27)-(30)；
3rd section to the 4th section of design method is：1. set the changeover portion region along axial length be respectively GD5 and GD6；2. determine changeover portion edge circular section and the abscissa Za5 and Za6, Za5=N of blade intersection point1+N2+N3- GD5, Za6=N1 +N2+N3+GD6；3. determine the abscissa rate of change of the break b relative to Za5 and Za6：Draw change Abscissa expression formulas of the break b of change in changeover portion：Zb=Za+H1+ △ 5 × [Za- (N1+N2+N3- GD5)], b point ordinates Calculated in the 3rd section of cylinder according to formula (30), in the 4th section of cylinder, convolution (22) obtains expression formula：Wb=R × sin (ηn)-K1
4. the d point abscissa rates of change relative to Za5 and Za6 are determined, Draw abscissa expression formulas of the top end point d of change in changeover portion：Zd=Za+S- △ 6 × [Za- (N1+N2+N3- GD5)], and Convolution (21), (23), (25) and (30) draws ordinate of the d points relative to Za5 and Za6：It is in the 3rd section of cylinder：It is in the 4th section of cylinder：By This, determines the top end point d of changeover portion change ordinate linear change rate, isDraw the top of change Ordinate expression formulas of the point d in changeover portion：[Za- (the N of Wd=Wd5+ △ 71+N2+N3-GD5)]；5. a points are horizontal, ordinate is in mistake The coordinate value crossed in section, is calculated at the 3rd section according to formula (27), (28), is calculated at the 4th section according to formula (21), (22)；
In above-mentioned each step：Za is drawn according to the calculation expression of a points abscissa on each section of helical blade.
Further, when the cylinder is three sections of cylinders, according to above-mentioned 2nd section to the 3rd section and the 3rd section to the 4th section of design side Method determines changeover portion region.
Further, the blade is discharge blade and the blade that is connected with feed pipe in the feed pipe punishment of prostomum section, A diameter of Dg1=470-500mm, a diameter of Dg2=480-510mm of ttom of pipe at the feed pipe mouth of pipe are set, then feeds length of tube Lg For：
The design method of its discharge blade is：
Length of the discharge blade on tubular axis direction is set as Zg, Zg=170-210mm, elemental height Ko, Ko =140-160mm, the distance for terminating height and charging pipe outer wall is K3-K2, takes 1 break b, each point a, b, c seat on blade Marking expression way is respectively：A (Za, Wa) point coordinates values calculate according to formula (13), (14), and b (Zb, Wb) point coordinates expression formula is：
Blade tip c points are relative to a point height B1 expression formulas：
Then c (Zc, Wc) point coordinates expression formula is：
Wc=Wa-B1
The blade design method that is connected with feed pipe is：
Its length of blade that is connected with feed pipe L is：L=Lg-Zg, takes two break b on blade, c, each point a on blade, B, c, d coordinate expression way are respectively：A (Za, Wa) point, b (Zb, Wb) point coordinates values according to formula (13), (14), (15), (16) calculate,
C (Zc, Wc) point coordinates expression formula is：
Zc=Za+S
Wc=Wa-B2+K3-K2
Blade tip d points are relative to a point height B2 expression formulas：
Then d (Zd, Wd) point coordinates expression formula is：
Zd=Za+S-H2
Wd=Wa-B2.
Further, GD1~GD6 spans are respectively 150-400mm.
The beneficial effects of the invention are as follows：
1. the stirring vane made using helix equation of the present invention, has good fitting performance.Become using the present invention The stirring vane of shape, has a more superior engagement fairness, and uniformity in stirring, all has in terms of the remaining rate of discharging Have an enormous advantage.
2. the design of discharge blade of the present invention at discharge nozzle, discharging speed is fast, is not easy to form buildup.
3. the present invention can take into account the performance requirement of blade stirring and discharging, and cause different cylinder section inside spin paddles The linear variation relation of helical angle of piece, the helix in so different cylinder sections is formed in cylinder junction to be seamlessly transitted, and is protected The continuity of helix has been demonstrate,proved, concrete can be also effectively prevented from and be bonded in such position.It can effectively improve The task performance of concrete mixer truck.
Brief description of the drawings
Fig. 1 is overall structure diagram of the present invention.
Fig. 2 is tube structure parameter schematic diagram of the present invention.
Fig. 3 is each cylinder section blade profile schematic shapes of the present invention.
Fig. 4 is the coordinate schematic diagram that present invention stirring barrel structure helicoid bus turns to put on face projection and blade.
In figure：1. stirring vane；2. inner cone section first paragraph cylinder；3. inner cone section second segment cylinder；4. stage casing cylindrical tube； 5. section cylinder, 6. feed pipes are bored after.
Embodiment
The present invention is described in further detail with reference to the accompanying drawings and examples.
Embodiment 1：As shown in figure 1, the present invention is used for the design of concrete stirring vane, the helical angle and blade-shaped of blade Shape can realize the consecutive variations from nozzle to cylinder bottom, and can be seamlessly transitted each section of cylinder junction according to each section of cylinder function.
The present invention comprises the following steps：
The first step：According to plane isogonism log spiral R=R0×ekθ, according to its property k=cot β, the relation drawn Formula：
R'/R=k=cot β (1)
Wherein, R is polar diameter, and θ is polar angle, R0To originate polar diameter, R is set0=1, k are constant, and β is helical angle, and R' represents R To θ derivations, e is mathematics Euler's constant, is the truth of a matter of natural logrithm function；
Second step：As shown in Fig. 2 according to formula (1) by changing its K value, K values span is 0.25~0.36, to change Become helixangleβ, set cone section cylinder nozzle as at minor diameter, cylinder bottom is at major diameter, if the k values of each section of cylinder nozzle and cylinder bottom are kj, j=1,2,3 ... n+1, n are the hop count of mixing drum, and this example selection n=4, setting nozzle cone section blade starting k values are k1= 0.25, it is k that cylinder base cone section blade, which terminates k values,5=0.32, make k1With k5Along cylinder axis direction linear change, k values are obtained along cylinder axle The interconversion rate PP in line direction is：
Wherein Ni, i=1,2 ... n, represent each section of cylinder axis direction length, this example N1=1600mm, N2= 1000mm, N3=1200mm, N4=1200mm；
K value k of each section of cylinder in junction is determined according to formula (2)j, i.e.,：J=2,3,4：
3rd step：As shown in Fig. 2 setting DlFor the diameter of mixing drum nozzle, cylinder bottom and each section of cylinder junction, l=1,2 ... n+1；Set inner cone section R2m-1For polar diameter corresponding to nozzle, inner cone section R2mFor polar diameter corresponding to cylinder bottom；Base cone section R2n-1For cylinder bottom Corresponding polar diameter, base cone section R2nFor polar diameter corresponding to nozzle, make the k values of each cone section cylinder change along polar diameter R dimension linears, obtain each Bore section cylinder k value changes rates Pm：
In formula：Inner cone section：
Base cone section：
ηmFor it is each cone section circular cone element line angle, m=1,2 ... n, m ≠ n-1,
I.e.：
In formula：
This example D1=1150mm, D2=2040mm, D3=D4=2348mm, D5=1800mm；
The circular cone section spiral line differential equation is obtained according to formula (1) and formula (4)：
kmEach cone section cylinder starting k values are represented, i.e.,：k1、k2、k3、k4；
Cylindrical section cylinder blade curve replaces log spiral using variable slope curve, using the k values of cylindrical section cylinder as exhibition The slope of open curve, make k values linear change vertically；Obtain
Cylindrical section cylinder k value changes rates：I.e.：
The cylinder section spiral line differential equation is obtained according to the functional relation of formula (6) and the slope of curve：
4th step：Obtaining each helix equation for boring section cylinder by formula (5) is：
By formula R=R0×ekθ, R0=1, obtain in formulaM=1,2 ... 4, m ≠ 3；
Show that the helix equation of cylindrical section cylinder is by formula (6), (7)：
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 from change Amount, y is dependent variable.
According to this example helix equation, stirring vane can have a variety of design methods, and this example uses existing blade shape Constant helical blades design method designs.
Embodiment 2：The helical blades that this example is changed using blade shape, each section of cylinder blade profile shape are as shown in Figure 3. The helix equation of section cylinder and cylindrical section cylinder is respectively bored according to blade in embodiment 1, the coordinate of blade each point is calculated；When described During each section of blade shape difference, specific method is：
Reference picture 4, using the nozzle center of circle of mixing drum as the origin of coordinates, using the central axis of mixing drum as Z axis, and with charging Direction for just, due to blade in cylinder helically surface state, so using the cylindrical-coordinate system using Z axis as dead axle line, radius side To coordinate represent that the anglec of rotation is represented with Fa with W, rotated in units of degree, and by left hand helix direction,
Parameter expression mode of the helical blade under this coordinate system be：A dynamic point A on barrel is selected in, the point is with helical-blade The helical curve of blade is drawn in piece anglec of rotation Fa change on barrel,
According to formula (8), using θ as independent variable, R is dependent variable, and conversion obtains trajectory equations of the dynamic point A on cone section cylinder For：
In formula θ be curve along cylinder deploy when corresponding polar angle, unit is radian, and its conversion with anglec of rotation Fa is closed It is to be：
Wherein：M=1,2,4, abbreviation obtains：
The point a being located at for inner cone section helical blade on helical curve, corresponding to Fa, the parameter of its Z axis and radial direction Coordinate is (Za, Wa)；According to formula (10), (12), the coordinate expressions for drawing a points on blade are：
Wa=R × sin (ηm) (14)
Wherein m=1,2 ... n-2=1,2,
The inner cone section blade takes two middle breaks, respectively b, c, corresponding to Fa b, c point coordinate be respectively (Zb, Wb), (Zc, Wc), coordinate expressions convolution (13), (14) obtain：
Wb=R × sin (ηm)-K1 (16)
Wherein m=1,2 ... n-2=1,2,
Wc=R × sin (ηm)-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, and the d point coordinates corresponding to Fa is (Zd, Wd), coordinate expressions convolution (13), (14)：
Wd=R × sin (ηm)-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, break is not taken, the angle of blade and cylinder diametric(al) line is γ, and span is： γ=10-24 °, this example γ=21 °, the coordinate of blade bottom arbitrfary point a and top arbitrfary point d corresponding to Fa be respectively (Za, Wa), (Zd, Wd), convolution (10), (12), the coordinate expressions for drawing a points are：
Za=N1+…+Nn-(R-R2n)×cos(ηn)=N1+…+N4-(R-R8)×cos(η4) (21)
Wa=R × sin (ηn)=R × sin (η4) (22)
D points are along cylinder axis direction linear change, its expression formula relative to a height B
K4, K5, G are empirical value in formula, and value is respectively：K4=300mm, K5=170mm, G=200mm；Then convolution (21), (22), (23), the coordinate expressions for drawing d points are：
Zd=N1+…+Nn-(R-R2n)×cos(ηn)-B×Tan(γ) (24)
Wd=R × sin (ηn)-B (25)
Dynamic point A trajectory equation is identical with formula (9) helix equation in cylinder barrel segment, i.e.,：
Using x as independent variable, y is dependent variable
Wherein x and Fa transformational relation is：
Cylindrical section cylinder helical blade is located at the point a on helical curve, corresponding to Fa, the parameter coordinate of Z axis and radial direction For (Za, Wa)；Convolution (9), (26), the coordinate expressions for drawing a points are：
Za=N1+…+Nn-2+ y=N1+N2+y (27)
Wa=Dn-1/ 2=D3/2 (28)
A break b is taken for cylindrical section cylinder helical blade, the coordinate corresponding to Fa b points is respectively (Zb, Wb), and it is sat Scale value expression formula convolution (27), (28) obtain：
Zb=N1+…+Nn-2+y+H1 (29)
Wb=Dn-1/2-K1 (30)
D is vane tip arbitrfary point, and the d point coordinates corresponding to Fa is (Zd, Wd), convolution (27), (28), draws d points Coordinate expressions be：
Zd=N1+…+Nn-2+y+S (31)
Wd=Dn-1/2-K3。 (32)
The anglec of rotation Fa changing methods of the blade：It is determined that the 1st section to the 3rd section cylinder the blade anglec of rotation Fa when, Fa exists Each section of cylinder tube port position changes since 0 degree, sets intermediate variable：M1, M2, each section of cylinder leaf of the 1st section to the n-th -2 sections cylinders of record Piece helix is rotated to the anglec of rotation Fa actual numerical values at each section of cylinder cylinder bottom, each section of cylinder blade anglec of rotation Fa actual numerical value expression formula For that is,：FaIt is real：
1st section：FaIt is real=Fa
2nd section：FaIt is real=Fa+M1
3rd section：FaIt is real=Fa+Mn-2=Fa+M2
Wherein Fa increases since 0 degree successively in each section of cylinder according to step-length, sets change step ii=1 degree, i.e.,：Fa=Fa + ii, until each section of cylinder blade screw line is rotated to each section of cylinder cylinder bottom；
Tail cone section cylinder anglec of rotation Fa changing methods：
It is to change from cylinder bottom to nozzle, therefore tail cone section cylinder anglec of rotation Fa exists because tail cone section cylinder is according to coordinate system direction It is to be changed by cylinder bottom to nozzle during actual calculating.Set Ta and change to a bottom anglec of rotation as tail cone section cylinder blade from nozzle, To distinguish Fa, Ta increases successively from 0 degree according to step-length, draws the anglec of rotation Ta at the end of blade screw line arrival cylinder bottom, is designated as M4, therefore, it is determined that during Fa, according to the anglec of rotation M drawn from cylinder bottom to nozzle4Reduced successively according to step-length, Fa=Fa-ii, directly Most 0, setting intermediate variable M3, record blade screw line rotated to the anglec of rotation Fa actual numerical values at the last period cylinder cylinder bottom, then tail Boring section cylinder Fa actual numerical value expression formulas is：
N-th section：FaIt is real=Mn-1+Mn- Fa=M3+M4-Fa。
In each section of cylinder junction both sides, changeover portion region, the changeover portion region blade arc both ends and two are set Blade arc joint in the cylinder of each section of side seamlessly transits.
When the cylinder hop count is four sections of cylinders, its 1st section to the 2nd section design method is：1. set the edge in the changeover portion region Axial length is respectively GD1 and GD2, as shown in Figure 3；2. determine changeover portion edge circular section and blade intersection point abscissa Za1 and Za2, Za1=N1- GD1, Za2=N1+GD2；3. convolution (13), (20) determine the top end point d ordinates relative to Za1 and Za2, It is in 1st section of cylinder：It is in 2nd section of cylinder：It is 4. true Determine top end point d ordinate linear change rate, beDraw the top end point d ordinate tables of changeover portion change It is up to formula：[Za- (the N of Wd=Wd1+ △ 11- GD1)], the abscissa of d points calculates according to formula (19)；5. a, b, c point horizontal stroke, ordinate Calculated in changeover portion according to formula (13)-(18)；
2nd section to the 3rd section of design method is：1. set the changeover portion region is respectively GD3 and GD4 along axial length, As shown in Figure 3；2. determine changeover portion edge circular section and the abscissa Za3 and Za4, Za3=N of blade intersection point1+N2- GD3, Za4= N1+N2+GD4；3. determine the abscissa rate of change of the break c relative to Za3 and Za4： Go out abscissa expression formulas of the break c of change in changeover portion：Zc=Za+S+ △ 2 × [Za- (N1+N2- GD3)], c point ordinates Calculated in the 2nd section of cylinder according to formula (18), expression formula is in the 3rd section of cylinder：Wc=Dn-1/ 2-K2,4. determine relative to Za3 and Za4 d point abscissa rates of change,Draw abscissa expression of the top end point d of change in changeover portion Formula：Zd=Za+S-H2+ △ 3 × [Za- (N1+N2- GD3)], and convolution (13),
(20), (32) draw ordinate of the d points relative to Za3 and Za4：It is in the 2nd section of cylinder：It is in the 3rd section of cylinder：Thus, determine that changeover portion changes Top end point d ordinate linear change rate, beShow that the top end point d of change is vertical in changeover portion Coordinate expressions：[Za- (the N of Wd=Wd3+ △ 41+N2-GD3)]；5. a, b points are horizontal, coordinate value of the ordinate in changeover portion, the Calculate according to formula (13)-(16) in 2 sections of cylinders, calculated in the 3rd section of cylinder according to formula (27)-(30)；
3rd section to the 4th section of design method is：1. set the changeover portion region along axial length be respectively GD5 and GD6, as shown in Figure 3；2. determine changeover portion edge circular section and the abscissa Za5 and Za6, Za5=N of blade intersection point1+N2+N3- GD5, Za6=N1+N2+N3+GD6；3. determine the abscissa rate of change of the break b relative to Za5 and Za6：Draw abscissa expression formulas of the break b of change in changeover portion：Zb=Za+H1+ △ 5 × [Za- (N1+N2+N3- GD5)], b point ordinates calculate in the 3rd section of cylinder according to formula (30), and in the 4th section of cylinder, convolution (22) obtains table Up to formula：Wb=R × sin (ηn) 4.-K1 determines d point abscissa rates of change relative to Za3 and Za4,Draw abscissa expression of the top end point d of change in changeover portion Formula：Zd=Za+S- △ 6 × [Za- (N1+N2+N3- GD5)], and convolution (21), (23), (25) and (30) draw d points relative to Za5 and Za6 ordinate expression formula：It is in the 3rd section of cylinder：It is in the 4th section of cylinder：Thus, determine the top end point d's of changeover portion change Ordinate linear change rate, it isDraw ordinate expression formulas of the top end point d of change in changeover portion： [Za- (the N of Wd=Wd5+ △ 71+N2+N3-GD5)]；5. a points are horizontal, coordinate value of the ordinate in changeover portion, at the 3rd section according to formula (27), (28) calculate, and are calculated at the 4th section according to formula (21), (22)；
In above-mentioned each step：Za is drawn according to the calculation expression of a points abscissa 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；
The blade is discharge blade and the blade that is connected with feed pipe in the feed pipe punishment of prostomum section, sets feed pipe A diameter of Dg1=488mm at the mouth of pipe, a diameter of Dg2=496.9mm of ttom of pipe,
Then charging length of tube is：
The design method of its discharge blade is：
Length of the discharge blade on tubular axis direction is set as Zg=200mm, elemental height Ko=150mm, eventually Only the distance of height and charging pipe outer wall be K3-K2, takes 1 break b, each point a, b, c coordinate expression way are distinguished on blade Calculated for a (Za, Wa) point coordinates values according to formula (13), (14), b (Zb, Wb) point coordinates expression formula is：
Blade tip c points are relative to a point height B1 expression formulas：
Then c (Zc, Wc) point coordinates expression formula is：
Wc=Wa-B1
Its blade design method that is connected with feed pipe is：
Its length of blade that is connected with feed pipe L is L=Lg-Zg, takes two break b on blade, c, each point a on blade, B, c, d coordinate expression way are respectively：A (Za, Wa) point, b (Zb, Wb) point coordinates values according to formula (13), (14), (15), (16) calculate,
C (Zc, Wc) point coordinates expression formula is：
Zc=Za+S
Wc=Wa-B2+K3-K2
Blade tip d points are relative to a point height B2 expression formulas：
Then d (Zd, Wd) point coordinates expression formula is：
Zd=Za+S-H2
Wd=Wd-B2.
The helical blade obtained according to the helical blade design method of the present invention, it is two in mixing drum internal helical blades, Interlaced 180 ° of placements.
Embodiment 3：This example is as different from Example 2：When the cylinder is three sections of cylinders, changeover portion is according to institute in embodiment 2 State the 2nd section of design method to the 3rd section and the 3rd section to the 4th section and determine changeover portion region.Wherein each parameter is：H1=20mm, K1 =70mm；K2=280mm；S=10mm；H2=60mm, K3=400mm；γ=18 °, K4=280mm, K5=150mm, G= 180mm；The change step ii=10 degree.Each section of transition section length be respectively：GD1=200mm, GD2=200mm, GD3= 200mm, GD4=200mm.Dg1=470mm, Dg2=480mm, Zg=185mm, Ko=145mm.
Embodiment 4：This example is 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；The change step ii =20 degree.Each section of transition section length be respectively：GD1=200mm, GD2=200mm, GD3=200mm, GD4=200mm, GD5= 300mm, GD6=200mm；Dg1=500mm, Dg2=510mm, Zg=210mm, Ko=160mm.

Claims (9)

  1. A kind of 1. design method based on linear change helical angle concrete stirring vane, it is characterised in that：Blade from nozzle to Cylinder bottom consecutive variations, comprise the following steps：
    The first step：According to plane isogonism log spiral R=R0×ekθ, according to its property k=cot β, the relational expression drawn：
    R'/R=k=cot β (1)
    Wherein, R is polar diameter, and θ is polar angle, R0To originate polar diameter, R is set0=1, k are constant, and β is helical angle, and R' represents that R is asked θ Lead, e is mathematics Euler's constant, is the truth of a matter of natural logrithm function；
    Second step：According to formula (1) by changing its k value, its span is 0.25~0.36, to change helixangleβ, setting cone Section cylinder nozzle is at minor diameter, and cylinder bottom is at major diameter, if the k values of each section of cylinder nozzle and cylinder bottom are kj, j=1,2,3 ... n+ 1, n is the hop count of mixing drum, and n >=3 and n be integer, it is k that setting nozzle cone section blade, which originates k values,1, cylinder base cone section blade terminates k It is worth for kn+1, and kn+1＞ k1, make k1With kn+1Along cylinder axis direction linear change, interconversion rate PP of the k values along cylinder axis direction is obtained For：
    <mrow> <mi>P</mi> <mi>P</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Wherein Ni, i=1,2 ... n, represent each section of cylinder axis direction length；
    K value k of each section of cylinder in junction is determined according to formula (2)j, i.e.,：J=2,3 ... n：
    <mrow> <msub> <mi>k</mi> <mi>j</mi> </msub> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>P</mi> <mi>P</mi> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    3rd step：Set DlFor the diameter of mixing drum nozzle, cylinder bottom and each section of cylinder junction, l=1,2 ... n+1；Set inner cone section R2m-1For polar diameter corresponding to nozzle, inner cone section R2mFor polar diameter corresponding to cylinder bottom；Base cone section R2n-1For polar diameter, base cone corresponding to cylinder bottom Section R2nFor polar diameter corresponding to nozzle, make the k values of each cone section cylinder change along polar diameter R dimension linears, obtain each cone section cylinder k value changes rates Pm：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>k</mi> <mi>m</mi> </msub> </mrow> <mrow> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>...</mo> <mi>n</mi> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>m</mi> <mo>&amp;NotEqual;</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    In formula：Inner cone section：
    Base cone section：
    ηmFor it is each cone section circular cone element line angle, m=1,2 ... n, m ≠ n-1,
    The circular cone section spiral line differential equation is obtained according to formula (1) and formula (4)：
    <mrow> <mfrac> <msup> <mi>R</mi> <mo>&amp;prime;</mo> </msup> <mi>R</mi> </mfrac> <mo>=</mo> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>+</mo> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    kmEach cone section cylinder starting k values are represented, i.e.,：M=1,2 ... n, m ≠ n-1；
    Cylindrical section cylinder blade curve replaces log spiral using variable slope curve, and the k values of cylindrical section cylinder is bent as expansion The slope of line, make k values linear change vertically；Obtain
    Cylindrical section cylinder k value changes rates：
    The cylinder section spiral line differential equation is obtained according to the functional relation of formula (6) and the slope of curve：
    <mrow> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>k</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mi>y</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    4th step：Obtaining each helix equation for boring section cylinder by formula (5) is：
    <mrow> <mfrac> <mi>R</mi> <mrow> <mi>R</mi> <mo>+</mo> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>/</mo> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>&amp;times;</mo> <msup> <mi>e</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>m</mi> </msub> <mo>)</mo> <mo>&amp;times;</mo> <mo>(</mo> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    By formula R=R0×ekθ, R0=1, obtain in formulaM=1,2 ... n, m ≠ n-1；
    Show that the helix equation of cylindrical section cylinder is by formula (6), (7)：
    <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <msub> <mi>k</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mfrac> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <msub> <mi>P</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;times;</mo> <mi>x</mi> </mrow> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    Wherein x, y is plane coordinate system direction, and x is along cylindrical drum diametric(al), and y is cylindrical drum axis direction, and x is independent variable, y For dependent variable.
  2. 2. the design method according to claim 1 based on linear change helical angle concrete stirring vane, its feature exist In：During each section of blade shape difference, the helix equation of section cylinder and cylindrical section cylinder is respectively bored according to blade, blade is calculated The coordinate of each point:
    Using the nozzle center of circle of mixing drum as the origin of coordinates, using the central axis of mixing drum as Z axis, and using feedstock direction as just, adopt To the cylindrical-coordinate system that Z axis is dead axle line, the coordinate of radial direction represents that the anglec of rotation is represented with Fa with W, in units of degree, And rotated by left hand helix direction,
    Parameter expression mode of the helical blade under this coordinate system be：A dynamic point A on barrel is selected in, the point revolves with helical blade The helical curve of blade is drawn in corner Fa change on barrel,
    According to formula (8), using θ as independent variable, R is dependent variable, and conversion obtains trajectory equations of the dynamic point A on cone section cylinder and is：
    <mrow> <mi>R</mi> <mo>=</mo> <mfrac> <mrow> <mo>(</mo> <mfrac> <msub> <mi>k</mi> <mi>m</mi> </msub> <msub> <mi>P</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;times;</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>&amp;times;</mo> <msup> <mi>e</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>m</mi> </msub> <mo>)</mo> <mo>&amp;times;</mo> <mo>(</mo> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>&amp;times;</mo> <msup> <mi>e</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>m</mi> </msub> <mo>)</mo> <mo>&amp;times;</mo> <mo>(</mo> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>m</mi> </msub> <mo>&amp;times;</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    Wherein：M=1,2 ... n, m ≠ n-1,
    In formula θ be curve along cylinder deploy when corresponding polar angle, unit is radian, its transformational relation with anglec of rotation Fa For：
    <mrow> <mfrac> <mrow> <mi>&amp;theta;</mi> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>m</mi> </msub> </mrow> <mrow> <msub> <mi>D</mi> <mi>m</mi> </msub> <mo>/</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;times;</mo> <mn>180</mn> </mrow> </mfrac> <mo>&amp;times;</mo> <mfrac> <mn>180</mn> <mi>&amp;pi;</mi> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>F</mi> <mi>a</mi> </mrow> <mn>360</mn> </mfrac> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein m=1,2 ... n, m ≠ n-1,
    Abbreviation obtains：
    <mrow> <mi>&amp;theta;</mi> <mo>=</mo> <mfrac> <mrow> <mi>F</mi> <mi>a</mi> <mo>&amp;times;</mo> <msub> <mi>D</mi> <mi>m</mi> </msub> <mo>&amp;times;</mo> <mi>&amp;pi;</mi> </mrow> <mrow> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;times;</mo> <mn>360</mn> </mrow> </mfrac> <mo>+</mo> <msub> <mi>&amp;theta;</mi> <mi>m</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    The point a being located at for inner cone section helical blade on helical curve, corresponding to Fa, the parameter coordinate of its Z axis and radial direction For (Za, Wa)；According to formula (10), (12), the coordinate expressions for drawing a points on blade are：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>Z</mi> <mi>a</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>Z</mi> <mi>a</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>N</mi> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> 2
    Wa=R × sin (ηm) (14)
    Wherein m=1,2 ... n-2,
    Take two middle breaks, respectively b, c for preceding tapered end blade, corresponding to Fa b, c point coordinate be respectively (Zb, Wb), (Zc, Wc), coordinate expressions convolution (13), (14) obtain：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>Z</mi> <mi>b</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>H</mi> <mn>1</mn> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>Z</mi> <mi>b</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>N</mi> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>H</mi> <mn>1</mn> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
    Wb=R × sin (ηm)-K1 (16)
    Wherein m=1,2 ... n-2,
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>Z</mi> <mi>c</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>S</mi> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>Z</mi> <mi>c</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>N</mi> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>S</mi> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
    Wc=R × sin (ηm)-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, and the d point coordinates corresponding to Fa is (Zd, Wd), and coordinate expressions convolution (13), (14) obtain：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>Z</mi> <mi>d</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>S</mi> <mo>-</mo> <mi>H</mi> <mn>2</mn> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>Z</mi> <mi>d</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mn>2</mn> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>cos</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;eta;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>N</mi> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>S</mi> <mo>-</mo> <mi>H</mi> <mn>2</mn> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>
    Wd=R × sin (ηm)-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, break is not taken, the angle of blade and cylinder diametric(al) line is γ, and span is：γ= 10-24 °, coordinate respectively (Za, Wa), (Zd, the Wd) of blade bottom arbitrfary point a and top arbitrfary point d corresponding to Fa, with reference to Formula (10), (12), the coordinate expressions for drawing a points are：
    Za=N1+…+Nn-(R-R2n)×cos(ηn) (21)
    Wa=R × sin (ηn) (22)
    D points are along cylinder axis direction linear change, its expression formula relative to a height B
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>B</mi> <mo>=</mo> <mi>K</mi> <mn>3</mn> <mo>-</mo> <mfrac> <mrow> <mi>K</mi> <mn>3</mn> <mo>-</mo> <mi>K</mi> <mn>4</mn> </mrow> <mrow> <msub> <mi>N</mi> <mn>4</mn> </msub> <mo>-</mo> <mi>G</mi> </mrow> </mfrac> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mi>Z</mi> <mi>a</mi> <mo>-</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>&amp;le;</mo> <mi>Z</mi> <mi>a</mi> <mo>&amp;le;</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>4</mn> </msub> <mo>-</mo> <mi>G</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>B</mi> <mo>=</mo> <mi>K</mi> <mn>4</mn> <mo>-</mo> <mfrac> <mrow> <mi>K</mi> <mn>4</mn> <mo>-</mo> <mi>K</mi> <mn>5</mn> </mrow> <mi>G</mi> </mfrac> <mo>&amp;times;</mo> <mo>&amp;lsqb;</mo> <mi>Z</mi> <mi>a</mi> <mo>-</mo> <mrow> <mo>(</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>4</mn> </msub> <mo>-</mo> <mi>G</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>,</mo> <mi>Z</mi> <mi>a</mi> <mo>&amp;GreaterEqual;</mo> <msub> <mi>N</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>N</mi> <mn>4</mn> </msub> <mo>-</mo> <mi>G</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow>
    K4, K5, G are empirical value in formula, and span is respectively：K4=280-320mm, K5=150-200mm, G=180- 240mm；Then convolution (21), (22), (23), the coordinate expressions for drawing d points are：
    Zd=N1+…+Nn-(R-R2n)×cos(ηn)-B×Tan(γ) (24)
    Wd=R × sin (ηn)-B (25)
    Dynamic point A trajectory equation is identical with formula (9) helix equation in cylinder barrel segment, i.e.,：
    <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <msub> <mi>k</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mfrac> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <msub> <mi>P</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;times;</mo> <mi>x</mi> </mrow> </msup> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> 3
    Using x as independent variable, y is dependent variable
    Wherein x and Fa transformational relation is：
    <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mi>&amp;pi;</mi> <mo>&amp;times;</mo> <msub> <mi>D</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <mn>360</mn> </mfrac> <mo>&amp;times;</mo> <mi>F</mi> <mi>a</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>26</mn> <mo>)</mo> </mrow> </mrow>
    Cylindrical section cylinder helical blade is located at the point a on helical curve, and corresponding to Fa, the parameter coordinate of Z axis and radial direction is (Za, Wa)；Convolution (9), (26), the coordinate expressions for drawing a points are：
    Za=N1+…+Nn-2+y (27)
    Wa=Dn-1/2 (28)
    Take a break b for cylindrical section cylinder helical blade, corresponding to Fa b points coordinate be respectively (Zb, Wb), its coordinate value Expression formula convolution (27), (28) obtain：
    Zb=N1+…+Nn-2+y+H1 (29)
    Wb=Dn-1/2-K1 (30)
    D is vane tip arbitrfary point, and the d point coordinates corresponding to Fa is (Zd, Wd), convolution (27), (28), draws the seat of d points Marking expression formula is：
    Zd=N1+…+Nn-2+y+S (31)
    Wd=Dn-1/2-K3 (32)。
  3. 3. the design method according to claim 1 based on linear change helical angle concrete stirring vane, its feature exist In：The anglec of rotation Fa changing methods of the blade：It is determined that the 1st section to (n-1)th section cylinder the blade anglec of rotation Fa when, Fa is at each section Cylinder tube port position changes since 0 °, sets intermediate variable：M1, M2..., Mn-2, record each section of cylinder blade screw line and rotate to each The anglec of rotation Fa actual numerical values at section cylinder cylinder bottom, each section of cylinder blade anglec of rotation Fa actual numerical value expression formula be, i.e.,：FaIt is real：
    1st section：FaIt is real=Fa
    2nd section：FaIt is real=Fa+M1
    ………
    (n-1)th section：FaIt is real=Fa+Mn-2
    Wherein Fa increases since 0 successively in each section of cylinder according to step-length, sets change step ii, i.e.,：Fa=Fa+ii, until each Section cylinder blade screw line is rotated to each section of cylinder cylinder bottom；
    Tail cone section cylinder, i.e. n-th section of cylinder, anglec of rotation Fa changing methods：
    The anglec of rotation that Ta changes to a bottom as tail cone section cylinder blade from nozzle is set, Ta increases, drawn successively from 0 according to step-length Blade screw line reaches the anglec of rotation Ta at the end of cylinder bottom, is designated as Mn, it is determined that during Fa, according to the anglec of rotation M drawnnSo that Fa Reduced successively according to step-length from cylinder bottom to nozzle, Fa=Fa-ii, until be 0, setting intermediate variable Mn-1, record blade screw line Rotate to the last period cylinder cylinder bottom anglec of rotation Fa actual numerical values, then tail cone section cylinder Fa actual numerical value expression formulas be：
    N-th section：FaIt is real=Mn-1+Mn-Fa。
  4. 4. the design method according to claim 3 based on linear change helical angle concrete stirring vane, its feature exist In：The change step ii is more than 0 degree and is less than or equal to 20 degree.
  5. 5. the design method according to claim 2 based on linear change helical angle concrete stirring vane, its feature exist In：Changeover portion region is set in each section of cylinder junction both sides, the changeover portion region blade arc both ends and both sides are each Blade arc joint in section cylinder seamlessly transits.
  6. 6. the design method according to claim 5 based on linear change helical angle concrete stirring vane, its feature exist In：When the cylinder hop count is four sections of cylinders, its 1st section to the 2nd section design method is：1. set the changeover portion region along axis Length is respectively GD1 and GD2；2. determine changeover portion edge circular section and the abscissa Za1 and Za2, Za1=N of blade intersection point1- GD1, Za2=N1+GD2；3. convolution (13), (20) determine the top end point d ordinates relative to Za1 and Za2, in the 1st section of cylinder For：It is in 2nd section of cylinder：4. determine top End points d ordinate linear change rate, it isDraw the top end point d ordinate expression formulas of changeover portion change For：[Za- (the N of Wd=Wd1+ △ 11- GD1)], the abscissa of d points calculates according to formula (19)；5. a, b, c point horizontal stroke, ordinate are in mistake Cross in section and calculated according to formula (13)-(18)；
    2nd section to the 3rd section of design method is：1. set the changeover portion region is respectively GD3 and GD4 along axial length；② Determine the abscissa Za3 and Za4, Za3=N of changeover portion edge circular section and blade intersection point1+N2- GD3, Za4=N1+N2+GD4； 3. determine the abscissa rate of change of the break c relative to Za3 and Za4：Draw change Abscissa expression formulas of the break c in changeover portion：Zc=Za+S+ △ 2 × [Za- (N1+N2- GD3)], c point ordinates are at the 2nd section Calculated in cylinder according to formula (18), expression formula is in the 3rd section of cylinder：Wc=Dn-1/ 2-K2,4. determine the d points relative to Za3 and Za4 Abscissa rate of change,Draw abscissa expression formulas of the top end point d of change in changeover portion：Zd=Za+ S-H2+△3×[Za-(N1+N2- GD3)], and convolution (13), (20), (32) draw vertical seat of the d points relative to Za3 and Za4 Mark：It is in the 2nd section of cylinder：It is in the 3rd section of cylinder： Thus, the top end point d of changeover portion change ordinate linear change rate is determined, isDraw the top of change Ordinate expression formulas of the end points d in changeover portion：[Za- (the N of Wd=Wd3+ △ 41+N2-GD3)]；5. a, b points horizontal stroke, ordinate are in mistake The coordinate value crossed in section, calculate according to formula (13)-(16) in the 2nd section of cylinder, calculated in the 3rd section of cylinder according to formula (27)-(30)；
    3rd section to the 4th section of design method is：1. set the changeover portion region is respectively GD5 and GD6 along axial length；② Determine the abscissa Za5 and Za6, Za5=N of changeover portion edge circular section and blade intersection point1+N2+N3- GD5, Za6=N1+N2+N3+ GD6；3. determine the abscissa rate of change of the break b relative to Za5 and Za6：Draw the folding of change Abscissa expression formulas of the point b in changeover portion：Zb=Za+H1+ △ 5 × [Za- (N1+N2+N3- GD5)], b point ordinates are the 3rd Calculated in section cylinder according to formula (30), in the 4th section of cylinder, convolution (22) obtains expression formula：Wb=R × sin (ηn)-K1
    4. the d point abscissa rates of change relative to Za5 and Za6 are determined, Draw abscissa expression formulas of the top end point d of change in changeover portion：Zd=Za+S- △ 6 × [Za- (N1+N2+N3- GD5)], and Convolution (21), (23), (25) and (30) draws ordinate of the d points relative to Za5 and Za6：It is in the 3rd section of cylinder：It is in the 4th section of cylinder：By This, determines the top end point d of changeover portion change ordinate linear change rate, isDraw the top of change Ordinate expression formulas of the point d in changeover portion：[Za- (the N of Wd=Wd5+ △ 71+N2+N3-GD5)]；5. a points are horizontal, ordinate is in mistake The coordinate value crossed in section, is calculated at the 3rd section according to formula (27), (28), is calculated at the 4th section according to formula (21), (22)；
    In above-mentioned each step：Za is drawn according to the calculation expression of a points abscissa on each section of helical blade.
  7. 7. the design method according to claim 6 based on linear change helical angle concrete stirring vane, its feature exist In：It is true according to the 2nd section of design method to the 3rd section and the 3rd section to the 4th section described in claim 6 when the cylinder is three sections of cylinders Determine changeover portion region.
  8. 8. the design method according to claim 2 based on linear change helical angle concrete stirring vane, its feature exist In：The blade is discharge blade and the blade that is connected with feed pipe in the feed pipe punishment of prostomum section, sets the feed pipe mouth of pipe Locate a diameter of Dg1=470-500mm, a diameter of Dg2=480-510mm of ttom of pipe, then feeding length of tube Lg is：
    The design method of its discharge blade is：
    Length of the discharge blade on tubular axis direction is set as Zg, Zg=170-210mm, elemental height Ko, Ko= 140-160mm, the distance for terminating height and charging pipe outer wall is K3-K2, takes 1 break b, each point a, b, c coordinate on blade Expression way is respectively：A (Za, Wa) point coordinates values calculate according to formula (13), (14), and b (Zb, Wb) point coordinates expression formula is：
    <mrow> <mi>Z</mi> <mi>b</mi> <mo>=</mo> <mi>Z</mi> <mi>a</mi> <mo>+</mo> <mfrac> <mrow> <mi>H</mi> <mn>1</mn> <mo>&amp;times;</mo> <mi>Z</mi> <mi>a</mi> </mrow> <mrow> <mi>Z</mi> <mi>g</mi> <mo>+</mo> <mi>S</mi> </mrow> </mfrac> </mrow>
    <mrow> <mi>W</mi> <mi>b</mi> <mo>=</mo> <mi>W</mi> <mi>a</mi> <mo>-</mo> <mfrac> <mrow> <mi>K</mi> <mn>1</mn> <mo>-</mo> <mi>K</mi> <mi>o</mi> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>Z</mi> <mi>g</mi> <mo>+</mo> <mi>S</mi> </mrow> </mfrac> <mo>&amp;times;</mo> <mi>Z</mi> <mi>a</mi> <mo>-</mo> <mi>K</mi> <mi>o</mi> <mo>/</mo> <mn>2</mn> </mrow>
    Blade tip c points are relative to a point height B1 expression formulas：
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>B</mi> <mn>1</mn> <mo>=</mo> <mfrac> <mrow> <mi>Z</mi> <mi>a</mi> <mo>+</mo> <mi>Z</mi> <mi>a</mi> <mo>/</mo> <mrow> <mo>(</mo> <mi>Z</mi> <mi>g</mi> <mo>+</mo> <mi>S</mi> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <mi>S</mi> </mrow> <mrow> <mi>Z</mi> <mi>g</mi> </mrow> </mfrac> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <msub> <mi>D</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>D</mi> <mi>g</mi> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <mo>-</mo> <mi>K</mi> <mn>3</mn> <mo>+</mo> <mi>K</mi> <mn>2</mn> <mo>-</mo> <mrow> <mo>(</mo> <mi>Z</mi> <mi>g</mi> <mo>-</mo> <mi>H</mi> <mn>2</mn> <mo>)</mo> </mrow> <mfrac> <mrow> <mi>D</mi> <mi>g</mi> <mn>2</mn> <mo>-</mo> <mi>D</mi> <mi>g</mi> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mi>L</mi> <mi>g</mi> </mrow> </mfrac> <mo>-</mo> <mi>K</mi> <mi>o</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mi>Z</mi> <mi>a</mi> <mi> </mi> <msub> <mi>tan&amp;eta;</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>K</mi> <mi>o</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>
    Then c (Zc, Wc) point coordinates expression formula is：
    <mrow> <mi>Z</mi> <mi>c</mi> <mo>=</mo> <mi>Z</mi> <mi>a</mi> <mo>+</mo> <mfrac> <mrow> <mi>Z</mi> <mi>a</mi> </mrow> <mrow> <mi>Z</mi> <mi>g</mi> <mo>+</mo> <mi>S</mi> </mrow> </mfrac> <mo>&amp;times;</mo> <mi>S</mi> </mrow>
    Wc=Wa-B1
    The blade design method that is connected with feed pipe is：
    Its length of blade that is connected with feed pipe L is：L=Lg-Zg, takes two break b on blade, c, each point a, b on blade, c, D coordinate expression way is respectively：A (Za, Wa) point, b (Zb, Wb) point coordinates values are counted according to formula (13), (14), (15), (16) Calculate,
    C (Zc, Wc) point coordinates expression formula is：
    Zc=Za+S
    Wc=Wa-B2+K3-K2
    Blade tip d points are relative to a point height B2 expression formulas：
    <mrow> <mi>B</mi> <mn>2</mn> <mo>=</mo> <mfrac> <mrow> <msub> <mi>D</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>D</mi> <mi>g</mi> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> <mo>+</mo> <mi>Z</mi> <mi>a</mi> <mo>&amp;times;</mo> <msub> <mi>tan&amp;eta;</mi> <mn>1</mn> </msub> <mo>-</mo> <mo>&amp;lsqb;</mo> <mi>Z</mi> <mi>a</mi> <mo>-</mo> <mrow> <mo>(</mo> <mi>H</mi> <mn>2</mn> <mo>+</mo> <mi>S</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>&amp;times;</mo> <mfrac> <mrow> <mi>D</mi> <mi>g</mi> <mn>2</mn> <mo>-</mo> <mi>D</mi> <mi>g</mi> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mi>L</mi> <mi>g</mi> </mrow> </mfrac> </mrow>
    Then d (Zd, Wd) point coordinates expression formula is：
    Zd=Za+S-H2
    Wd=Wa-B2.
  9. 9. the design method according to claim 6 based on linear change helical angle concrete stirring vane, its feature exist In：GD1~GD6 spans are respectively 150-400mm.
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CN102555058A (en) * 2011-12-30 2012-07-11 中国重汽集团青岛重工有限公司 Spiral blade for concrete stirring tank
RU2456155C2 (en) * 2009-08-03 2012-07-20 Федеральное государственное образовательное учреждение высшего профессионального образования "Кубанский государственный аграрный университет" Concrete mixer (versions)
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