CN114491833B

CN114491833B - Parameterized rapid modeling method for tapered corrugated fin section radiator

Info

Publication number: CN114491833B
Application number: CN202111618494.6A
Authority: CN
Inventors: 郭佳; 刘志敏; 王武俊; 焦生金; 刘谆
Original assignee: CRRC Yongji Electric Co Ltd
Current assignee: CRRC Yongji Electric Co Ltd
Priority date: 2021-12-28
Filing date: 2021-12-28
Publication date: 2024-05-14
Anticipated expiration: 2041-12-28
Also published as: CN114491833A

Abstract

The invention relates to a modeling scheme of a section radiator, in particular to a parameterized rapid modeling method of a tapered corrugated fin section radiator. The invention aims at modeling of the air-cooled fin radiator in the application occasion of the medium-high power converter, in particular to simulation modeling of the radiator with the tapered corrugated fin section, adopts a parameterization mathematical modeling method to realize the rapid modeling functions of the radiator with the side ribs with different radiuses, different sizes of corrugated fin units, different tapered fins, different fin numbers, different substrate thicknesses, different fin offset distances and different sizes and shapes, and can automatically generate a three-dimensional model by software only by inputting key technical parameters, thereby improving the efficiency of three-dimensional modeling and simulation. And the comparison analysis of the heat dissipation performance of fin units with different shapes is convenient, and the optimal structural scheme is determined.

Description

Parameterized rapid modeling method for tapered corrugated fin section radiator

Technical Field

The invention relates to a modeling scheme of a section radiator, in particular to a parameterized rapid modeling method of a tapered corrugated fin section radiator.

Background

The converter is an important component of an alternating current transmission electric system, and the IGBT is used as a power component of a core of the converter and is a main heating source. High power converters are generally required to have high reliability, and excellent heat dissipation is an important guarantee for their proper operation. The high-loss power device is tightly contacted with the radiator, so that heat generated during operation is transferred to the radiator fins in a conduction mode and is further transferred to the outside through the fan. In the thermal design of electronic equipment, the profile radiator is widely applied due to the simple structure, convenient processing and good radiating effect.

In practical application, the heat resistance of the radiator is affected by a plurality of factors. How to comprehensively consider these factors so as to minimize the thermal resistance of the radiator under certain working conditions is an urgent problem to be solved in engineering design. Therefore, it is also necessary to optimally design the heat sink. The optimization of the radiator belongs to the constraint multivariable optimization problem, the objective function is generally radiator thermal resistance, and the optimization design variables can be rib length, rib height, rib spacing, rib number, rib shape and the like.

In the prior art, according to the three-dimensional structure of an actual profile radiator, three-dimensional graphic drawing software Preo/Creo or SCDM under Ansys WorkBench is adopted to carry out three-dimensional simulation modeling on the radiator. For a radiator composed of corrugated fin units of different size and shape combinations, it is necessary to redraw the three-dimensional model by re-using drawing software. Especially for corrugated fins with different taper grades, the taper angle needs to be calculated again according to measured fin data, and then drawing of corrugated fin units is carried out.

By adopting the radiator simulation modeling method, when modeling corrugated fin unit radiators with different conicity, different size and shape combinations, the modeling is complex, the workload is also great, and the simulation analysis efficiency is greatly reduced.

Disclosure of Invention

The invention provides a parameterized rapid modeling method for a radiator with a tapered corrugated fin profile, which aims to solve the technical problems that the existing radiator simulation modeling method is complex in modeling, large in workload and low in simulation analysis efficiency.

The parameterized rapid modeling method of the tapered corrugated fin section radiator comprises a fin part and a base plate part, wherein the fin part comprises a middle fin and an edge fin, and the structural characteristic expression of the corrugated fin section radiator is as follows: y=f (Φ (i), Φ (j), Φ (k)); phi (i) in the expression is a functional relation of the middle fin, phi (j) is a functional relation of the substrate part, and phi (k) is a functional relation of the edge fin; the construction of the corrugated fin profile radiator model comprises the following steps:

Step one, establishing a single corrugated fin unit model, wherein the offset distance, the circulation period and the taper angle of the circle centers of a large circle radius, a small circle radius and a large circle center of a corrugated fin unit in the vertical coordinate direction are respectively R, R, pit_ _ciry, n and alpha, a coordinate system is defined firstly, the positive direction of an X-axis of an abscissa is towards the left, and the positive direction of a Y-axis of an ordinate is upwards;

The three points of the single corrugated fin unit are sequentially O (x ₁,y₁)、A(x₂,y₂)、B(x₃,y₃) from bottom to top, and the three points respectively define the O point, the A point and the B point by taking a starting circle center C point (x ₀,y₀) of the corrugated fin unit as a reference, namely, the C point of the corrugated fin unit as a starting point coordinate of a coordinate system; for the corrugated fin unit model, the angle β of the corrugated fin unit is β=arcsin { pit_ _ciry/(r+r) } in value;

the corrugated fin unit model is distinguished by a large circle and a small circle according to the size of the curvature radius, and the structure of the small circle of the corrugated fin unit model under the upper/large circle is taken as an example for explanation;

When the corrugated fin unit has no taper, i.e. the taper angle alpha is 0, the coordinates of the C, O, A and B points in the corrugated fin unit as a function of R, r, beta and alpha are: y=f (R, cos, sin, β);

if the point A is on the left side of the point C, and the corrugated fin units have no taper, the abscissa of the point O, A, B is the same, and the coordinate expressions of the point O, the point A and the point B are respectively:

x₁= x₀+R*cosβ,y₁= y₀-R*sinβ；

x₂= x₀+R*cosβ,y₂= y₀+R*sinβ；

x₃= x₀+R*cosβ,y₃= y₀+(r+R)* sinβ+ r*sinβ=y₀+R*sinβ+ 2*r*sinβ;

If the point A is on the right side of the point C, and the corrugated fin units have no taper, the abscissa of the point O, A, B is the same, and the coordinate expressions of the point O, the point A and the point B are respectively:

x₁= x₀-R*cosβ,y₁= y₀-R*sinβ；

x₂= x₀-R*cosβ,y₂= y₀+R*sinβ；

x₃= x₀-R*cosβ,y₃= y₀+(r+R)* sinβ+ r*sinβ=y₀+R*sinβ+ 2*r*sinβ;

when the corrugated fin unit has taper and the taper angle is alpha, three points of the corrugated fin unit from bottom to top are sequentially O '(x ₁',y₁')、A'(x₂',y₂')、B'(x₃',y₃'), wherein the three points take a starting circle center C 'point (x ₀',y₀') of the corrugated fin unit as a reference, namely, the C 'point of the corrugated fin unit is taken as a coordinate system starting point coordinate, and the O' point, the A 'point and the B' point are respectively defined, so that the relation between the coordinates of the C ', O', the A 'point and the B' point in the corrugated fin unit and R, r, beta and alpha is as follows: y=f (R, cos, sin, β, α);

If the point A 'is left of the point O' and rotates clockwise, the coordinate expressions of the point C ', the point O', the point A 'and the point B' are respectively as follows:

x₀'=x₀*cos(α)- y₀*sin(α),y₀'= x₀*sin(α)+ y₀*cos(α)；

x₁'=x₀'+R*cos(β-α),y₁'=y₀'-R*sin(β-α)；

x₂'=x₀'+R*cos(β+α),y₂'=y₀'+R*sin(β+α)；

x₃'=x₀'+(r+R)*cos(β+α)- r*cos(β-α),y₃'= y₀'+(r+R)* sin(β+α)+ r*sin(β-α);

If the point a 'is left of the point O' and rotates counterclockwise, the coordinate expressions of the point C ', the point O', the point a 'and the point B' are respectively:

x₀'=x₀*cos(-α)- y₀*sin(-α),y₀'= x₀*sin(-α)+ y₀*cos(-α);

x₁'=x₀'+R*cos(β+α),y₁'=y₀'-R*sin(β+α)；

x₂'=x₀'+R*cos(β-α),y₂'=y₀'+R*sin(β-α)；

x₃'=x₀'+(r+R)*cos(β-α)- r*cos(β+α),y₃'= y₀'+(r+R)* sin(β-α)+ r*sin(β+α);

if the point A 'is on the right side of the point O' and rotates clockwise, the coordinate expressions of the point C ', the point O', the point A 'and the point B' are respectively as follows:

x₀'=x₀*cos(α)- y₀*sin(α),y₀'= x₀*sin(α)+ y₀*cos(α)；

x₁'=x₀'-R*cos(β+α),y₁'=y₀'-R*sin(β+α)；

x₂'=x₀'-R*cos(β-α),y₂'=y₀'+R*sin(β-α)；

x₃'=x₀'- (r+R)*cos(β-α)+ r*cos(β+α),y₃'= y₀'+(r+R)* sin(β-α)+ r*sin(β+α);

if the point A 'is on the right side of the point O' and rotates anticlockwise, the coordinate expressions of the point C ', the point O', the point A 'and the point B' are respectively as follows:

x₀'=x₀*cos(-α)- y₀*sin(-α),y₀'= x₀*sin(-α)+ y₀*cos(-α);

x₁'=x₀'-R*cos(β-α),y₁'=y₀'-R*sin(β-α)；

x₂'=x₀'-R*cos(β+α),y₂'=y₀'+R*sin(β+α)；

x₃'=x₀'-(r+R)*cos(β+α)+ r*cos(β-α),y₃'= y₀'+(r+R)* sin(β+α)+ r*sin(β-α).

Step two, on the basis of a single corrugated fin unit in the step one, a plurality of corrugated fin unit models of a single fin are built, the C 'point of the corrugated fin unit model is taken as a reference point, the length of C' C ² 'is taken as an offset interval, cyclic iteration is carried out according to the cyclic period n as the number of corrugated fin units, the number of the corrugated fin units refers to the number of the corrugated fin units counted from the C' point, a plurality of corrugated fin unit models are built, and the functional relation of the reference points (C ', C ²',……Cⁿ') in the plurality of corrugated fin unit models is as follows: y=f (pit_ _ciry, n, cos, sin, α), x ₀ ⁿ 'is taken as the abscissa of the n-th corrugated fin unit C ⁿ' point, y ₀ ⁿ 'is taken as the ordinate of the n-th corrugated fin unit C ⁿ' point, and x ₀ ⁿ= x₀,y₀ ⁿ= y₀+(n-1)*2* Pit__ciry is taken as the ,x₀ ⁿ'= x₀ ⁿcos(-α)- y₀ ⁿsin(-α),y₀ ⁿ'= x₀ ⁿsin(-α)+ y₀ ⁿcos(-α); in the formula of ,x₀ ⁿ'= x₀ ⁿcos(α)- y₀ ⁿsin(α),y₀ ⁿ'= x₀ ⁿsin(α)+ y₀ ⁿcos(α); when the model rotates clockwise and when the model rotates counterclockwise; the coordinates of the O ⁿ ' point, the A ⁿ ' point and the B ⁿ ' point in the nth corrugated fin unit are determined and refer to the functional relation between the O ', the A ', the B ' point and the C ' in the first step;

when n is an integer, establishing n corrugated fin unit models by utilizing the functional relation of the datum points in the corrugated fin unit models in the second step and the functional relation of O ', A', B 'points and C' points in the first step;

When n is not an integer, there are three cases:

The first case is that the top is more than half teeth, firstly, a function relation of datum points in a plurality of corrugated fin unit models in the second step and a function relation of O ', A', B 'points and C' in the first step are utilized to establish [ n ] corrugated fin unit models, wherein [ n ] represents that n is the largest integer smaller than n, then, the top is defined for more half teeth, and the top coordinates of the more half teeth are A ^[n]+1'(x₂ ^[n]+1', y₂ ^[n]+1'),A^[n]+1 'coordinates which need to be determined on the basis of the datum points C ^[n]+1'(x₀ ^[n ^]+1', y₀ ^[n]+1' of [ n ] +1 corrugated fin units;

If the point a 'is left of the point C' and rotates clockwise, the top coordinates a ^[n]+1 'of the top half teeth of the plurality of corrugated fin unit models and the coordinate expression of the point C ^[n]+1' are respectively:

x₀ ^[n]+1'=x₀ ^[n]+1cos(α)- y₀ ^[n]+1sin(α),y₀ ^[n]+1'= x₀ ^[n]+1sin(α)+ y₀ ^[n]+1cos(α);

x₂ ^[n]+1'=x₀ ^[n]+1'+R *cos(β+α),y₂ ^[n]+1'=y₀ ^[n]+1'+ R *sin(β+α);

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

If the point a 'is left of the point C' and rotates counterclockwise, the top coordinates a ^[n]+1 'of the top half teeth of the plurality of corrugated fin unit models and the coordinate expressions of the point C ^[n]+1' are respectively:

x₀ ^[n]+1'=x₀ ^[n]+1cos(-α)- y₀ ^[n]+1sin(-α),y₀ ^[n]+1'= x₀ ^[n]+1sin(-α)+ y₀ ^[n]+1cos(-α);

x₂ ^[n]+1'=x₀ ^[n]+1'+R *cos(β-α),y₂ ^[n]+1'=y₀ ^[n]+1'+ R *sin(β-α);

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

If the point a 'is on the right side of the point C' and rotates clockwise, the coordinate expressions of the top coordinates a ^[n]+1 'and the point C ^[n]+1' of the top half teeth of the plurality of corrugated fin unit models are respectively:

x₂ ^[n]+1'=x₀ ^[n]+1'-R *cos(β-α),y₂ ^[n]+1'=y₀ ^[n]+1'+ R *sin(β-α);

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

If the point a 'is to the right of the point C' and rotates counterclockwise, the coordinate expressions of the top coordinates a ^[n]+1 'and the point C ^[n]+1' of the top half teeth of the plurality of corrugated fin unit models are respectively:

x₂ ^[n]+1'=x₀ ^[n]+1'-R *cos(β+α),y₂ ^[n]+1'=y₀ ^[n]+1'+ R *sin(β+α);

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

The second condition is that the bottom is more than half teeth, firstly, a function relation of datum points in the corrugated fin unit models in the second step and a function relation of O ', A ', B ' points and C ' in the first step are utilized to build [ n ] corrugated fin unit models, wherein [ n ] represents that n is the largest integer smaller than n, then, definition is carried out on half teeth with more bottoms, and the bottom coordinates of the half teeth with more bottoms are A ^-1' (x₁ ^-1', y₁ ^-1 ');

If the point a ' is left of the point C ' and rotates clockwise, the bottom end points a ^-1 ' of the bottom half teeth of the plurality of corrugated fin unit models are:

x₁ ^-1'= x₀'+ (R+r)*cos(β-α) - r*cos(β+α),y₁ ^-1'= y₀'- (R+r)*sin(β-α) - r*sin(β+α);

If the point a ' is left of the point C ' and rotates counterclockwise, the bottom end points a ^-1 ' of the bottom half teeth of the plurality of corrugated fin unit models are:

x₁ ^-1'= x₀'+ (R+r)*cos(β+α) - r*cos(β-α),y₁ ^-1'= y₀'- (R+r)* sin(β+α) - r* sin(β-α);

If the point a ' is to the right of the point C ' and rotates clockwise, the bottom end points a ^-1 ' of the bottom half teeth of the plurality of corrugated fin unit models are:

x₁ ^-1'= x₀'- (R+r)* cos(β+α) + r* cos(β-α),y₁ ^-1'= y₀'- (R+r)* sin(β+α) - r* sin(β-α);

if the point a ' is to the right of the point C ' and is rotated counterclockwise, the bottom end points a ^-1 ' of the bottom half teeth of the plurality of corrugated fin unit models are:

x₁ ^-1'= x₀'- (R+r)* cos(β-α)+r* cos(β+α),y₁ ^-1'= y₀'- (R+r)* sin(β-α) - r*sin(β+α);

The third case is that the top and bottom are more than half teeth, namely, the coordinate expression of the vertex endpoint A ^[n]+1 'of the top more than half teeth and the bottom endpoint A ^-1' of the bottom more than half teeth in the multiple corrugated fin unit models is determined by using the functional relation of the two cases.

Step three, the joint of the bottom of the single intermediate fin and the radiating substrate is set as a straight tooth, on the basis of the plurality of corrugated fin unit models in the step two, the intersection point coordinate of the bottom of the single intermediate fin and the substrate is determined to be H (x ₄,y₄), the straight tooth length of the bottom of the single intermediate fin is taken as L_ _downfin, the ordinate of the tail end point of the plurality of corrugated fin unit models is taken as gamma_ _down, the abscissa of the tail end point of the plurality of corrugated fin unit models is taken as X_ _down, and the function relation of the intersection point coordinate H point of the bottom of the fin and the substrate is as follows: y=f (l_ _downfin, n, γ__down, χ__down);

when n is an integer, γ_ _down and χ_ _down are the ordinate y ₁ 'and the abscissa x ₁', respectively, of the O '(x ₁',y₁') point of the 1 st corrugated fin unit;

When n is not an integer, there are three cases:

In the first case, for the top half of the teeth, γ_ _down and χ_ _down are the ordinate y ₁ 'and abscissa x ₁', respectively, of the O '(x ₁',y₁') point of the 1 st corrugated fin unit;

In the second case, for more than half of the teeth at the bottom, gamma _down and χ _down are the bottom end points of more than half of the teeth at the bottom, respectively

The ordinate y ₁ ^-1 ' and the abscissa x ₁ ^-1 ' of the point a ^-1' (x₁ ^-1', y₁ ^-1 ');

In the third case, for more than half teeth at the top and bottom, γ_ _down and χ_ _down are the ordinate y ₁ ^-1 ' and abscissa x ₁ ^-1 ', respectively, of the bottom end point a ^-1' (x₁ ^-1', y₁ ^-1 ') of the bottom most half tooth;

The coordinate relation of the intersection point H (x ₄,y₄) of the bottom of the fin and the substrate is:

x₄=χ__down,y₄=γ__down- L__downfin。

Step four, determining the coordinate of a top endpoint of the fin, namely a top semicircle endpoint, as an ordinate y ₄ of an intersection point coordinate H (x ₄,y₄) point of the bottom of the single intermediate fin and the substrate in the step three based on the plurality of corrugated fin unit models established in the step two, wherein the coordinate of the top semicircle endpoint is I (x ₅,y₅), taking the height of the single intermediate fin as H_ _fin, taking the radius of the top semicircle as r_ _semi, taking the vertex abscissa of the plurality of corrugated fin unit models as χ_ _up, and the functional relation of the coordinate I point of the top endpoint of the fin is: y=f (h_ _fin, r__semi, n,χ__up);

When n is an integer, χ_ _up is the abscissa x ₃ ⁿ 'of the point B ⁿ'(x₃ ⁿ',y₃ ⁿ' of the nth corrugated fin unit;

When n is not an integer, there are three cases:

In the first case, χ_ _up is the abscissa x ₂ ^[n]+1 'of the A ^[n]+1'(x₂ ^[n ^]+1', y₂ ^[n]+1' point of the [ n ] +1 corrugated fin unit for the top half of the teeth;

In the second case, χ_ _up is the abscissa x ₃ ^[n] 'of the point B ^[n]' (x₃ ^[n]',y₃ ^[n]' of the [ n ] th corrugated fin unit for more than half teeth at the bottom;

In the third case, χ_ _up is the abscissa x ₂ ^[n]+1 'of the [ n ] +1th corrugated fin unit A ^[n ^]+1'(x₂ ^[n]+1', y₂ ^[n]+1') point for more than half teeth at the top and bottom;

The coordinate relationship of the point of coordinate I (x ₅,y₅) of the fin top end point is:

x₅=χ__up,y₅= y₄+(H__fin- r__semi)。

Step five, according to the above steps one to four, the construction of the half structure in the three-dimensional model of the single intermediate fin can be completed, namely, the right half structure of the single intermediate fin or the left half structure of the single intermediate fin, for convenience of subsequent description, the construction of the right half structure in the three-dimensional model of the single intermediate fin is completed according to the above steps one to four, on the basis of the right half structure, the thickness of the single intermediate fin is taken to be Th_ _fin, then the function relation of the left half structure in the single intermediate fin is y=f(Th__fin, R,r,cos,sin,β,α, n, Pit__ciry, L__downfin, γ__down, χ__down, H__fin, r__semi, χ__up);, the reference point coordinates C _λ' (x_0λ',y_0λ 'of the corrugated fin unit in the left half structure of the single intermediate fin are firstly determined, the rest point coordinates (the coordinates of O _λ'、A_λ' and B _λ 'of the corrugated fin unit of the left half structure, the coordinates of A _λ ^[n]+1' and A _λ ^-1 'of the corrugated fin unit, the intersection point H _λ coordinate of the fin bottom contacted with the substrate, and the endpoint coordinate I _λ of the fin top end point are all constructed on the reference point C _λ', and the construction process is the step one to step four;

When the single middle fin has taper, the right half structure and the left half structure are both close to the middle, namely, when the structure on one side rotates clockwise, the structure on the other side rotates anticlockwise; for a single middle fin with taper, the right half structure of the middle fin rotates anticlockwise, and the left half structure rotates clockwise;

according to the left and right half side structure relation of the single middle fin, the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin units in the left half side structure has the following two conditions:

the first case is that the number of corrugated fin units of the left and right half structures of the single intermediate fin is equal, that is, n is the same, and then the following four cases exist in the functional relation of the reference point coordinates C _λ' (x_0λ',y_0λ') of the corrugated fin units in the left half structure:

a, the left and right half structures are parallel, and the point A ' is at the left side of the point C ', the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin units in the left half structure is as follows:

x_0λ'= x₀'+Th__fin+R_right*cos(β+α)- R_left*cos(β-α),y_0λ'= y₀'；

b, the left and right half structures are parallel, and the point A ' is on the right side of the point C ', the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left half structure is as follows:

x_0λ'= x₀'+Th__fin+ R_left *cos(β+α)- R_right *cos(β-α),y_0λ'= y₀';

C, the left and right half structures are symmetrical and the bottom ends are retracted, and the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin units in the left half structure is as follows:

x_0λ'= x₀'+Th__fin- R_left *cos(β-α)- R_right *cos(β-α),y_0λ'= y₀';

d, symmetrical left and right half structures and outward expansion of the bottom end, and the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin units in the left half structure is as follows:

x_0λ'= x₀'+Th__fin+ R_left *cos(β+α)+ R_right *cos(β+α),y_0λ'= y₀';

The second condition is that the number of corrugated fin units of the left half structure and the right half structure of the single middle fin is unequal, namely n is unequal, and the following two main conditions exist in the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ') of the corrugated fin units in the left half structure;

In the first case, the half teeth at the bottom end of one side of the left and right half structures are outwards expanded, and the cases are specifically divided into the following four cases:

a, the first corrugated fin unit of the left-right half structure is parallel, and the point A ' is at the left side of the point C ', and then the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left-right half structure is as follows:

x_0λ'= x₀'+Th__fin+2*R_right*cos(β+α)-(R_left+ R_right )*cos(β-α),y_0λ'= y₀';

b, the first corrugated fin unit of the left-right half structure is parallel, and the point A ' is at the right side of the point C ', the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left-right half structure is as follows:

x_0λ'= x₀'+Th__fin+2*R_left *cos(β+α)-(R_left+ R_right )*cos(β-α),y_0λ'= y₀';

C, the first corrugated fin unit of the left-right half structure is symmetrical, and the bottom end of the left-half structure is provided with a plurality of teeth, the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin unit in the left-half structure is as follows:

x_0λ'= x₀'+Th__fin- (2* R_right+R_left) *cos(β-α)+R_right *cos(β+α),y_0λ'= y₀';

d, the first corrugated fin unit of the left-right half structure is symmetrical, and the bottom end of the right half structure is provided with a plurality of teeth, the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin unit in the left half structure is as follows:

x_0λ'= x₀'+Th__fin- (2* R_left + R_right) *cos(β-α)+R_left *cos(β+α),y_0λ'= y₀';

in the second case, the half teeth at the bottom end of one side of the left and right half structures shrink inwards, and the two cases are specifically divided into the following four cases:

x_0λ'= x₀'+Th__fin- 2*R_left*cos(β-α) +(R_left+ R_right )*cos(β+α),y_0λ'= y₀';

x_0λ'= x₀'+Th__fin- 2*R_right *cos(β-α) +(R_left+ R_right )*cos(β+α),y_0λ'= y₀';

x_0λ'= x₀'+Th__fin+(2* R_right+R_left) *cos(β+α) - R_right *cos(β-α),y_0λ'= y₀';

x_0λ'= x₀'+Th__fin+ (2* R_left + R_right) *cos(β+α) - R_left *cos(β-α),y_0λ'= y₀';

In the fifth embodiment, r_right and r_left are the radii of curvature of the arcs O ' a ' and O _λ'A_λ ' of the first corrugated fin unit in the right/left half structure, respectively.

Step six, according to the above-mentioned step one to step five, can finish the construction of the single intermediate fin structure; based on a single intermediate fin, according to the structural combination characteristics of two adjacent groups of fins, taking the fin spacing as pit_ _fin and the fin number as N, the three-dimensional functional relation y=f (R, r, cos, sin, β, α, n, Pit__ciry, L__downfin, γ__down, χ__down, H__fin, r__semi, χ__up,Th__fin,Pit__fin,N) of all the intermediate fins has the following two conditions:

The first case is that the number of corrugated fin units of the left and right half structures of a single intermediate fin is equal, namely N is the same, the single intermediate fin phi (i) is defined as an integral unit, with the single intermediate fin phi (i) as a reference, pit_ _fin+Th__fin is an offset interval, iteration is carried out according to the number N (odd-even unlimited) of the fins, and a three-dimensional model of all intermediate fins of the radiator is established, wherein the functional relationship is as follows:

φ(i)= φ(i)single+N*(Pit__fin+Th__fin)；

The second case is that the number of corrugated fin units of the left and right half structures of the single intermediate fin is unequal, namely n is unequal, and the two cases are divided into two cases:

a, defining a single intermediate fin phi (i) as an integral unit, taking the single intermediate fin phi (i) as a reference, taking Pit_ _fin+Th__fin as an offset interval, iterating according to the number N (odd-even unlimited) of fins, and establishing a three-dimensional model of all intermediate fins of the radiator;

b, constructing another symmetrical fin phi (i) single_ _reverse by utilizing the constructed single intermediate fin phi (i) single, and constructing a three-dimensional model of all intermediate fins of the radiator by means of mathematical function relation f { (x ₄+ Th__fin+ Pit__fin/2)+ x}=f{(x₄+ Th__fin+ Pit__fin/2) -x }, namely about x=x ₄+ Th__fin+ Pit__fin/2 axisymmetry, based on an abscissa x ₄ in an intersection point coordinate H (x ₄,y₄) of the bottom of the single intermediate fin in the step three, wherein 2 x (Pit_ _fin+Th__fin) is an offset distance based on the single intermediate fin phi (i), and the three-dimensional model of all intermediate fins of the radiator is constructed by taking the two fins as an integral unit, wherein the number N/2 (N is an even number) of the fins:

φ(i)= {φ(i)single, φ(i)single__reverse}+N/2*2*(Pit__fin+Th__fin)。

Step seven, determining a substrate structure based on the intermediate fin group structure constructed in the step one to the step six; taking the width of the substrate as wid_ _base, the thickness of the substrate as Th_ _base and the length of the substrate as L_ _base, the functional relationship of the substrate part model is as follows:

φ(j) = f (Wid__base, Th__base, L__base)；

Determining four endpoint coordinates of the substrate as K (x ₆,y₆)、L(x₇,y₇)、M(x₈,y₈) and N (x ₉,y₉); based on the intersection point coordinate H (x ₄,y₄) of the bottom of the single middle fin contacted with the substrate in the third step, taking the distance between the intersection point coordinate H ₁(x_4-1,y_4-1) point of the bottom of the head end fin of the middle fin contacted with the substrate and the K point of the edge end point of the substrate as offset, and obtaining the functional relation of the four end points of the substrate as follows ：x₆=x_4-1-offset,y₆=y_4-1; x₇=x₆+L__base=x_4-1-offset+L__base,y₇=y_4-1;

x₈=x₇=x_4-1-offset+L__base,y₈= y_4-1-Th__base; x₉= x₆= x_4-1-offset,y₉=y₈= y_4-1-Th__base;

The functional relation of the distance offset between the intersection point coordinate H ₁(x_4-1,y_4-1) point of the bottom of the head end fin of the middle fin and the substrate, and the end point K point of the edge of the substrate is as follows:

offset = {L__base- Th__fin- (N-1)*( Pit__fin+Th__fin)} /2。

step eight, based on the first seven steps, after the construction of the middle fin group and the base plate is completed, modeling of the edge fins is finally performed, namely, the edge fins are arranged on two sides of the middle fin group, and the modeling is divided into the following two cases:

The first case is that the edge fin is a straight-edge trapezoidal structure, four end points of the right-edge straight-edge trapezoidal fin are determined to be K (x ₆,y₆)、P(x₁₀,y₁₀)、Q(x₁₁,y₁₁) and R (x ₁₂,y₁₂), wherein the end point K (x ₆,y₆) of the trapezoidal fin is coincident with the end point K (x ₆,y₆) in the substrate structure; based on the ordinate y ₅ of the endpoint coordinate I point of the top semicircle of the fin and the radius r_ _semi of the top semicircle in the fourth step, taking the top length of the edge trapezoidal fin as L_ _trape__up and the bottom length of the trapezoidal fin as L_ _trape__down, the functional relationship of the edge fin is as follows: phi (k) =f (l_ _{trape_up}, L__{trape_down}); the remaining three endpoints P (x ₁₀,y₁₀)、Q(x₁₁,y₁₁) and R (x ₁₂,y₁₂) of the right-side trapezoidal fin have the following functional relationship:

x₁₀= x₆+L__{trape_down},y₁₀= y₆;x₁₁= x₆+L__{trape_up},y₁₁= y₅+r__semi;x₁₂= x₆,y₁₂= y₅+r__semi;

For the left-side edge straight-edge trapezoidal fin structure, another symmetrical left-side edge straight-edge trapezoidal fin structure is constructed by utilizing the constructed right-side edge straight-edge trapezoidal fin according to the abscissa x ₆ in the endpoint coordinates K (x ₆,y₆) of the right-side trapezoidal fin through the mathematical function relation f { (x ₆ + L__base /2)+ x}=f{( x₆+ L__base/2) -x }, namely, the structural symmetry is about an x=x ₆+ L__base/2 axis;

the second case is that the edge fin is a corrugated fin trapezoid structure, and the construction method is that on the basis of the first case of the straight-edge trapezoid fin, the inner straight edge PQ of the edge fin is replaced by the combination of a plurality of corrugated fin units and straight edges; determining four end point coordinates of a right edge corrugated fin trapezoid as K (x ₆,y₆)、P(x₁₀,y₁₀)、Q(x₁₁,y₁₁) and R (x ₁₂,y₁₂), determining a starting point coordinate of intersection of a plurality of corrugated fin units and straight edges in the inner side of the edge corrugated fin trapezoid as P ₁(x₁₃,y₁₃, overlapping reference points C' _trape of the plurality of corrugated fin units with P ₁ points, and enabling a modeling method of the plurality of corrugated fin units to be consistent with a multi-corrugated fin unit modeling method of a middle single fin in the first step; taking distances between an inner side endpoint P of the edge corrugated fin trapezoid and starting points P ₁ of a plurality of corrugated fin units in the directions of an x axis and a y axis as Dx_ _trape and Dy_ _trape respectively, taking offset distances, cycle periods and cone angles of circle centers of large circle radius, small circle radius and large circle radius of the edge corrugated fin trapezoid in the direction of an ordinate as R_ _trape、r__trape、Pit__ciry__trape、n__trape and alpha_ _trape respectively, wherein the coordinate relation formula of the points of the starting point coordinates P ₁(x₁₃,y₁₃) of the right edge corrugated fin trapezoid structure is that the construction function relation of the right edge corrugated fin trapezoid structure is ：φ(k) = f (Dx__trape, Dy__trape,L__{trape_up}, L__{trape_down}, R__trape, r__trape, Pit_ciry__trape, n__trape, α__trape); is that:

x₁₃= x₁₀-Dx__trape,y₁₃= y₁₀+Dy__trape；

For the left-side edge corrugated fin trapezoid structure, another symmetrical left-side edge corrugated fin trapezoid structure is constructed by utilizing the constructed right-side edge corrugated fin trapezoid based on the abscissa x ₆ in the endpoint coordinates K (x ₆,y₆) of the right-side trapezoid fin through the mathematical function relation f { (x ₆ + L__base /2)+ x}=f{( x₆+ L__base/2) -x }, namely, the trapezoid structure is symmetrical about an x=x ₆+ L__base/2 axis;

and (3) according to the steps one to eight, the construction of the corrugated fin section radiator model can be completed.

The invention aims at modeling of the air-cooled fin radiator in the application occasion of the medium-high power converter, in particular to simulation modeling of the radiator with the tapered corrugated fin section, adopts a parameterization mathematical modeling method to realize the rapid modeling functions of the radiator with the side ribs with different radiuses, different sizes of corrugated fin units, different tapered fins, different fin numbers, different substrate thicknesses, different fin offset distances and different sizes and shapes, and can automatically generate a three-dimensional model by software only by inputting key technical parameters, thereby improving the efficiency of three-dimensional modeling and simulation. And the comparison analysis of the heat dissipation performance of fin units with different shapes is convenient, and the optimal structural scheme is determined.

The rapid simulation modeling method for the radiator can be used for conveniently and rapidly performing simulation modeling on the radiator with the taper corrugated fin profile with different taper angles, different size and shape combinations, saves simulation modeling time, improves simulation analysis efficiency and solves the problem of difficult modeling of a complex model.

Drawings

Fig. 1 schematic diagram of a corrugated fin unit no-taper (α=0) model (this figure is accompanied by a schematic of angle β), (1) a to the left of C; (2) A to the right of C.

FIG. 2 is a schematic diagram of a model of a corrugated fin unit with a taper and A (A ') to the left of C (C'), rotated (1) clockwise; (2) counterclockwise rotation.

FIG. 3 is a schematic diagram of a model of a corrugated fin unit with taper and A (A ') to the right of C (C'). (1) rotating clockwise; (2) counterclockwise rotation.

The number n of corrugated fin units in fig. 4 is not an integer and is a schematic view of the top most of the teeth. (1) point A 'is to the left of point C' and rotates clockwise; (2) point A 'is to the left of point C' and is rotated counterclockwise; (3) the point A 'is right of the point C' and rotates clockwise; and (4) the point A 'is right to the point C' and rotates anticlockwise.

The number n of corrugated fin units in fig. 5 is not an integer and the bottom is a schematic view of a plurality of teeth. (1) point A 'is to the left of point C' and rotates clockwise; (2) point A 'is to the left of point C' and is rotated counterclockwise; (3) the point A 'is right of the point C' and rotates clockwise; and (4) the point A 'is right to the point C' and rotates anticlockwise.

FIG. 6 is a schematic diagram of a middle single fin model, top half circle endpoint I and bottom endpoint H.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 7 is equal, and the relative positions of the arc fin unit datum points C 'and C _λ' when the left and right half structures are parallel and the point a 'is on the left side of the point C'. The meanings of (1) - (5) in fig. 7-18 are as follows: (1) the left and right sides are both small circles at the upper part and the lower part of the large circle; (2) the left and right sides are both big circles under the upper/lower circles; (3) the radii of the big circle and the small circle on the left side and the right side are the same; (4) Left small circle on top/big circle under-right big circle under top/small circle; (5) Left big circle on top/small circle under-right small circle under top/big circle.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 8 is equal, and the relative positions of the arc fin unit datum points C 'and C _λ' when the left and right half structures are parallel and the point a 'is on the right side of the point C'.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 9 is equal, the left and right half structures are symmetrical, and the relative positions of the reference points C 'and C _λ' of the arc fin units are shown when the bottom ends are retracted.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 10 is equal, and the relative positions of the reference points C 'and C _λ' of the arc fin units when the left and right half structures are symmetrical and the bottom ends are expanded outwards are shown schematically.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 11 is not equal, half teeth at the bottom end of one side of the left and right half structures are outwards expanded, and the first corrugated fin unit in the left and right half structures is parallel, and the relative positions of the reference points C 'and C _λ' of the arc fin units when the point a 'is at the left side of the point C'.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 12 is not equal, half teeth at the bottom end of one side of the left and right half structures are outwards expanded, and the first corrugated fin unit in the left and right half structures is parallel, and the relative positions of the reference points C 'and C _λ' of the arc fin units are shown when the point a 'is on the right side of the point C'.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 13 is not equal, half teeth at the bottom end of one side of the left and right half structures are outwards expanded, and the first corrugated fin unit in the left and right half structures is symmetrical, and the relative positions of the arc fin unit datum points C 'and C _λ' are shown when the bottom end of the left half structure is provided with a plurality of teeth.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 14 is not equal, half teeth at the bottom end of one side of the left and right half structures are outwards expanded, and the first corrugated fin unit in the left and right half structures is symmetrical, and the relative positions of the arc fin unit datum points C 'and C _λ' are shown when the bottom end of the right half structure is provided with a plurality of teeth.

In fig. 15, the number of corrugated fin units in the left and right half structures of the single intermediate fin is not equal, the half teeth at the bottom end of one side of the left and right half structures are retracted inwards, the first corrugated fin unit in the left and right half structures is parallel, and the reference points C 'and C _λ' of the arc fin units are shown in the schematic diagram when the point a 'is left of the point C'.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 16 is not equal, the half teeth at the bottom end of one side of the left and right half structures are retracted inwards, and the first corrugated fin unit in the left and right half structures is parallel, and the relative positions of the reference points C 'and C _λ' of the arc fin units are shown when the point a 'is on the right side of the point C'.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 17 is not equal, one half tooth at the bottom end of one side of the left and right half structures is contracted inwards, the first corrugated fin unit in the left and right half structures is symmetrical, and the relative positions of the arc fin unit datum points C 'and C _λ' are shown when the bottom end of the left half structure is provided with a plurality of half teeth.

The number of corrugated fin units in the left and right half structures of the single intermediate fin in fig. 18 is not equal, one half tooth at the bottom end of one side of the left and right half structures is retracted inwards, and the first corrugated fin unit in the left and right half structures is symmetrical, and the relative positions of the arc fin unit datum points C 'and C _λ' are shown when the bottom end of the right half structure is provided with a plurality of half teeth.

Fig. 19 is a schematic view of the structure of the intermediate fin group. (1) The number of corrugated fin units of the left and right half structures of the single middle fin is equal-the structure of each fin is the same; (2) The number of corrugated fin units of the left and right half structures of the single middle fin is not equal-the structure of each fin is the same; (3) The number of corrugated fin units of the left and right half structures of the single middle fin is unequal, and the structures of two adjacent groups of single fins are mirror images.

FIG. 20 is a schematic diagram of the construction of the intermediate fin set and the base plate.

Fig. 21 is a schematic construction diagram of a straight-sided trapezoidal structure.

Fig. 22 is a schematic construction diagram of a corrugated fin trapezoid structure.

Fig. 23 is a diagram of six different corrugated fin profile radiator models constructed by a parameterized rapid modeling method of a tapered corrugated fin profile radiator according to the present invention.

Detailed Description

The parameterized rapid modeling method of the tapered corrugated fin section radiator comprises a fin part and a base plate part, wherein the fin part comprises a middle fin and an edge fin, and the structural characteristic expression of the corrugated fin section radiator is as follows: y=f (Φ (i), Φ (j), Φ (k)); in the expression, phi (i) is a functional relation of the middle fin, phi (j) is a functional relation of the base plate part, phi (k) is a functional relation of the edge fin, and the construction of the corrugated fin section radiator model comprises the following steps:

As shown in fig. 1 (1), if point a is on the left side of point C and the abscissa of O, A, B points is the same because the corrugated fin unit has no taper, the coordinate expressions of point O, point a and point B are respectively:

x₁= x₀+R*cosβ,y₁= y₀-R*sinβ；

x₂= x₀+R*cosβ,y₂= y₀+R*sinβ；

x₃= x₀+R*cosβ,y₃= y₀+(r+R)* sinβ+ r*sinβ=y₀+R*sinβ+ 2*r*sinβ;

As shown in fig. 1 (2), if point a is on the right side of point C and the abscissa of O, A, B points is the same because the corrugated fin unit has no taper, the coordinate expressions of point O, point a and point B are respectively:

x₁= x₀-R*cosβ,y₁= y₀-R*sinβ；

x₂= x₀-R*cosβ,y₂= y₀+R*sinβ；

x₃= x₀-R*cosβ,y₃= y₀+(r+R)* sinβ+ r*sinβ=y₀+R*sinβ+ 2*r*sinβ;

As shown in fig. 2 (1), if the a 'point is left of the O' point and rotates clockwise, the coordinate expressions of the C 'point, the O' point, the a 'point, and the B' point are respectively:

x₀'=x₀*cos(α)- y₀*sin(α),y₀'= x₀*sin(α)+ y₀*cos(α)；

x₁'=x₀'+R*cos(β-α),y₁'=y₀'-R*sin(β-α)；

x₂'=x₀'+R*cos(β+α),y₂'=y₀'+R*sin(β+α)；

as shown in fig. 2 (2), if the a 'point is left of the O' point and rotates counterclockwise, the coordinate expressions of the C 'point, the O' point, the a 'point, and the B' point are respectively:

x₀'=x₀*cos(-α)- y₀*sin(-α),y₀'= x₀*sin(-α)+ y₀*cos(-α);

x₁'=x₀'+R*cos(β+α),y₁'=y₀'-R*sin(β+α)；

x₂'=x₀'+R*cos(β-α),y₂'=y₀'+R*sin(β-α)；

As shown in fig. 3 (1), if the a 'point is on the right side of the O' point and rotates clockwise, the coordinate expressions of the C 'point, the O' point, the a 'point, and the B' point are respectively:

x₀'=x₀*cos(α)- y₀*sin(α),y₀'= x₀*sin(α)+ y₀*cos(α)；

x₁'=x₀'-R*cos(β+α),y₁'=y₀'-R*sin(β+α)；

x₂'=x₀'-R*cos(β-α),y₂'=y₀'+R*sin(β-α)；

as shown in fig. 3 (2), if the a 'point is on the right side of the O' point and rotates counterclockwise, the coordinate expressions of the C 'point, the O' point, the a 'point, and the B' point are respectively:

x₀'=x₀*cos(-α)- y₀*sin(-α),y₀'= x₀*sin(-α)+ y₀*cos(-α);

x₁'=x₀'-R*cos(β-α),y₁'=y₀'-R*sin(β-α)；

x₂'=x₀'-R*cos(β+α),y₂'=y₀'+R*sin(β+α)；

Step two, for the mathematical expression in the two cases of whether the taper exists above, the expression in the case of the taper can be completely adopted, if no taper exists, alpha=0 is required, the corrugated fin units with the taper as alpha are taken as examples for illustration, and the non-taper fins are required to have the alpha=0; on the basis of a single corrugated fin unit, a plurality of corrugated fin unit models of a single fin are built, the point C 'of the corrugated fin unit model is taken as a reference point, the length of C' C ² 'is taken as an offset interval, cyclic iteration is carried out according to the cyclic period n as the number of the corrugated fin units, the number of the corrugated fin units refers to the number of the corrugated fin units counted from the point C', a plurality of corrugated fin unit models are built, and the functional relation of the reference points (C ', C ²',……Cⁿ') in the plurality of corrugated fin unit models is as follows: y=f (pit_ _ciry, n, cos, sin, α), x ₀ ⁿ 'is taken as the abscissa of the n-th corrugated fin unit C ⁿ' point, y ₀ ⁿ 'is taken as the ordinate of the n-th corrugated fin unit C ⁿ' point, and x ₀ ⁿ= x₀,y₀ ⁿ= y₀+(n-1)*2* Pit__ciry is taken as the ,x₀ ⁿ'= x₀ ⁿcos(-α)- y₀ ⁿsin(-α),y₀ ⁿ'= x₀ ⁿsin(-α)+ y₀ ⁿcos(-α); in the formula of ,x₀ ⁿ'= x₀ ⁿcos(α)- y₀ ⁿsin(α),y₀ ⁿ'= x₀ ⁿsin(α)+ y₀ ⁿcos(α); when the model rotates clockwise and when the model rotates counterclockwise; the coordinates of the O ⁿ ' point, the A ⁿ ' point and the B ⁿ ' point in the nth corrugated fin unit are determined and refer to the functional relationship between the O ', the A ', the B ' point and the C ' in the first step;

When n is not an integer, there are three cases:

As shown in fig. 4 (1), if the point a 'is left of the point C' and rotates clockwise, the top coordinates a ^[n]+1 'of the top half teeth of the plurality of corrugated fin unit models and the coordinate expression of the point C ^[n]+1' are respectively:

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

As shown in fig. 4 (2), if the point a 'is left of the point C' and rotates counterclockwise, the top coordinates a ^[n]+1 'of the top half teeth and the coordinate expressions of the point C ^[n]+1' of the plurality of corrugated fin unit models are respectively:

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

As shown in fig. 4 (3), if the point a 'is on the right side of the point C' and is rotated clockwise, the top coordinates a ^[n]+1 'of the top half teeth of the plurality of corrugated fin unit models and the coordinate expressions of the point C ^[n]+1' are respectively:

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

As shown in fig. 4 (4), if the point a 'is on the right side of the point C' and is rotated counterclockwise, the top coordinates a ^[n]+1 'of the top half teeth and the coordinate expressions of the point C ^[n]+1' of the plurality of corrugated fin unit models are respectively:

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

As shown in fig. 5 (1), if the point a ' is left of the point C ' and rotates clockwise, the bottom end points a ^-1 ' of the bottom half teeth of the plurality of corrugated fin unit models are:

x₁ ^-1'= x₀'+ (R+r)*cos(β-α)- r*cos(β+α),y₁ ^-1'= y₀'- (R+r)*sin(β-α) - r*sin(β+α);

as shown in fig. 5 (2), if the point a ' is left of the point C ' and rotates counterclockwise, the bottom end points a ^-1 ' of the bottom half teeth of the plurality of corrugated fin unit models are:

As shown in fig. 5 (3), if the point a ' is on the right side of the point C ' and rotates clockwise, the bottom end points a ^-1 ' of the bottom half teeth of the plurality of corrugated fin unit models are:

as shown in fig. 5 (4), if the point a ' is on the right side of the point C ' and rotates counterclockwise, the bottom end points a ^-1 ' of the bottom half teeth of the plurality of corrugated fin unit models are:

When n is an integer, γ_ _down and χ_ _down are the ordinate y ₁ 'and the abscissa x ₀', respectively, of the O '(x ₁',y₁') point of the 1 st corrugated fin unit;

When n is not an integer, there are three cases:

x₄=χ__down,y₄=γ__down- L__downfin；

Fourth, referring to fig. 6, based on the multiple corrugated fin unit models established in the second step and the ordinate y ₄ of the point of intersection point coordinates H (x ₄,y₄) where the bottom of the single intermediate fin contacts with the substrate in the third step, determining the coordinates of the top endpoint of the fin, that is, the top semicircle endpoint, as I (x ₅,y₅), taking the height of the single intermediate fin as h_ _fin, taking the radius of the top semicircle as r_ _semi, taking the vertex abscissa of the multiple corrugated fin unit models as χ_ _up, and the functional relation of the coordinates of the point I of the top endpoint of the fin is: y=f (h_ _fin, r__semi, n,χ__up);

When n is not an integer, there are three cases:

x₅=χ__up,y₅= y₄+(H__fin- r__semi)。

a, as shown in FIG. 7, the left and right half structures are parallel and the point A ' is at the left side of the point C ', and the functional relation of the reference point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left half structure is:

x_0λ'= x₀'+Th__fin+R_right*cos(β+α)- R_left*cos(β-α),y_0λ'= y₀'；

b, as shown in FIG. 8, the left and right half structures are parallel and the point A ' is at the right side of the point C ', and then the functional relation of the reference point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left half structure is:

x_0λ'= x₀'+Th__fin+ R_left *cos(β+α)- R_right *cos(β-α),y_0λ'= y₀';

And C, as shown in fig. 9, the left and right half structures are symmetrical and the bottom ends are retracted, and the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin units in the left half structure is as follows:

x_0λ'= x₀'+Th__fin- R_left *cos(β-α)- R_right *cos(β-α),y_0λ'= y₀';

d, as shown in fig. 10, the left and right half structures are symmetrical and the bottom ends are expanded outwards, and then the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin units in the left half structure is as follows:

x_0λ'= x₀'+Th__fin+ R_left *cos(β+α)+ R_right *cos(β+α),y_0λ'= y₀';

a, as shown in FIG. 11, the first corrugated fin unit of the left-right half structure is parallel and the point A ' is at the left side of the point C ', and then the functional relation of the reference point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left-half structure is:

b, as shown in FIG. 12, the first corrugated fin unit of the left-right half structure is parallel and the point A ' is at the right side of the point C ', and then the functional relation of the reference point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left-half structure is:

and C, as shown in FIG. 13, the first corrugated fin unit of the left-right half structure is symmetrical, and the bottom end of the left-half structure is more than half teeth, then the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin unit in the left-half structure is as follows:

d, as shown in fig. 14, the first corrugated fin unit of the left half structure and the right half structure are symmetrical, and the bottom end of the right half structure is more than half teeth, the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin unit in the left half structure is as follows:

a, as shown in FIG. 15, the first corrugated fin unit of the left-right half structure is parallel and the point A ' is at the left side of the point C ', and then the functional relation of the reference point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left-half structure is:

b, as shown in FIG. 16, the first corrugated fin unit of the left-right half structure is parallel and the point A ' is at the right side of the point C ', and then the functional relation of the reference point coordinates C _λ' (x_0λ',y_0λ ' of the corrugated fin unit in the left-half structure is:

x_0λ'= x₀'+Th__fin-2*R_right *cos(β-α) +(R_left+ R_right )*cos(β+α),y_0λ'= y₀';

And C, as shown in FIG. 17, the first corrugated fin unit of the left-right half structure is symmetrical, and the bottom end of the left-half structure is more than half teeth, then the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin unit in the left-half structure is as follows:

d, as shown in fig. 18, the first corrugated fin unit of the left half structure and the right half structure are symmetrical, and the bottom end of the right half structure is more than half teeth, the functional relation of the datum point coordinates C _λ' (x_0λ',y_0λ' of the corrugated fin unit in the left half structure is as follows:

In the fifth above-mentioned formulas, r_right and r_left are the radii of curvature of the arcs O ' a ' and O _λ'A_λ ' of the first corrugated fin unit in the right/left half structure, respectively.

In the first case, the number of corrugated fin units of the left and right half structures of the single intermediate fin is equal, namely N is the same, the single intermediate fin phi (i) single is defined as an integral unit, with the single intermediate fin phi (i) single as a reference, pit_ _fin+Th__fin is an offset interval, iteration is performed according to the number N (odd-even unlimited) of the fins, and a three-dimensional model of all intermediate fins of the radiator is built, as shown in fig. 19 (1), and the functional relationship is:

φ(i)= φ(i)single+N*(Pit__fin+Th__fin)；

a, defining a single intermediate fin phi (i) as an integral unit, taking the single intermediate fin phi (i) as a reference, taking Pit_ _fin+Th__fin as an offset interval, iterating according to the number N (odd-even unlimited) of fins, and establishing a three-dimensional model of all intermediate fins of the radiator, as shown in fig. 19 (2);

b, constructing another symmetrical fin phi (i) single_ _reverse by utilizing the constructed single intermediate fin phi (i) single, and constructing a three-dimensional model of all intermediate fins of the radiator by means of mathematical function relation f { (x ₄+ Th__fin+ Pit__fin/2)+ x}=f{(x₄+ Th__fin+ Pit__fin/2) -x }, namely about x=x ₄+ Th__fin+ Pit__fin/2 axisymmetry, based on an abscissa x ₄ in an intersection point coordinate H (x ₄,y₄) of the bottom of the single intermediate fin in the step three, wherein 2 (Pit_ _fin+Th__fin) is an offset distance based on the single intermediate fin phi (i), and the three-dimensional model of all intermediate fins of the radiator is built by taking the two fins as an integral unit and carrying out iteration according to the number N/2 (N is an even number) of the fins, wherein the function relation is as shown in fig. 19 (3):

φ(i)= {φ(i)single, φ(i)single__reverse}+N/2*2*(Pit__fin+Th__fin)。

φ(j) = f (Wid__base, Th__base, L__base)；

As shown in fig. 20, four end coordinates of the substrate are determined to be K (x ₆,y₆)、L(x₇,y₇)、M(x₈,y₈) and N (x ₉,y₉); based on the intersection point coordinate H (x ₄,y₄) of the bottom of the single middle fin contacted with the substrate in the third step, taking the distance between the intersection point coordinate H ₁(x_4-1,y_4-1) point of the bottom of the head end fin of the middle fin contacted with the substrate and the K point of the edge end point of the substrate as offset, and obtaining the functional relation of the four end points of the substrate as follows ：x₆=x_4-1-offset,y₆=y_4-1; x₇=x₆+L__base=x_4-1-offset+L__base,y₇=y_4-1;

offset = {L__base- Th__fin- (N-1)*( Pit__fin+Th__fin)} /2。

The first case is that the edge fin is a straight-sided trapezoidal structure, as shown in fig. 21, four end points of the right-sided straight-sided trapezoidal fin are determined to be K (x ₆,y₆)、P(x₁₀,y₁₀)、Q(x₁₁,y₁₁) and R (x ₁₂,y₁₂), wherein the end point K (x ₆,y₆) of the trapezoidal fin coincides with the end point K (x ₆,y₆) in the substrate structure; based on the ordinate y ₅ of the endpoint coordinate I point of the top semicircle of the fin and the radius r_ _semi of the top semicircle in the fourth step, taking the top length of the edge trapezoidal fin as L_ _trape__up and the bottom length of the trapezoidal fin as L_ _trape__down, the functional relationship of the edge fin is as follows: phi (k) =f (l_ _{trape_up}, L__{trape_down}); the remaining three endpoints P (x ₁₀,y₁₀)、Q(x₁₁,y₁₁) and R (x ₁₂,y₁₂) of the right-side trapezoidal fin have the following functional relationship:

The second case is that the edge fin is a corrugated fin trapezoid structure, as shown in fig. 22, the construction method is that the inner side straight edge PQ of the edge fin is replaced by a combination of a plurality of corrugated fin units and straight edges on the basis of the first case straight edge trapezoid fin; determining four end point coordinates of a right edge corrugated fin trapezoid as K (x ₆,y₆)、P(x₁₀,y₁₀)、Q(x₁₁,y₁₁) and R (x ₁₂,y₁₂), determining a starting point coordinate of intersection of a plurality of corrugated fin units and straight edges in the inner side of the edge corrugated fin trapezoid as P ₁(x₁₃,y₁₃, overlapping reference points C' _trape of the plurality of corrugated fin units with P ₁ points, and enabling a modeling method of the plurality of corrugated fin units to be consistent with a multi-corrugated fin unit modeling method of a middle single fin in the first step; taking distances between an inner side endpoint P of the edge corrugated fin trapezoid and starting points P ₁ of a plurality of corrugated fin units in the directions of an x axis and a y axis as Dx_ _trape and Dy_ _trape respectively, taking offset distances, cycle periods and cone angles of circle centers of large circle radius, small circle radius and large circle radius of the edge corrugated fin trapezoid in the direction of an ordinate as R_ _trape、r__trape、Pit__ciry__trape、n__trape and alpha_ _trape respectively, wherein the coordinate relation formula of the points of the starting point coordinates P ₁(x₁₃,y₁₃) of the right edge corrugated fin trapezoid structure is that the construction function relation of the right edge corrugated fin trapezoid structure is ：φ(k) = f (Dx__trape, Dy__trape,L__{trape_up}, L__{trape_down}, R__trape, r__trape, Pit_ciry__trape, n__trape, α__trape); is that:

x₁₃= x₁₀-Dx__trape,y₁₃= y₁₀+Dy__trape；

According to the design of the scheme, the three parts of the middle fin, the base plate and the edge fin are respectively subjected to mathematical modeling according to the three-dimensional structure of the real corrugated fin profile radiator with the taper and the characteristic of periodical repetition of the corrugated fins, so that the rapid modeling of the whole radiator is realized.

The technical key point of the invention

(1) Analyzing the structure of an actual corrugated fin profile radiator with taper, summarizing the geometric relationships of various shapes, and carrying out parameterized mathematical modeling;

(2) The method is suitable for general programs of various shapes, and can realize rapid parametric modeling of the rib profile radiator with different vertex angles, different sizes of corrugated fin units, different taper fins, different fin numbers, different substrate thicknesses, different fin offset distances and different sizes and shapes.

The modeling method can construct the non-taper corrugated fins shown in fig. 23 (1), wherein the middle fins of the fins are non-taper, the number of corrugated fin units on two sides of a single fin is different, and the edge fins are straight-edge trapezoidal fins. As shown in fig. 23 (2), the middle fin of the tapered corrugated fin has taper, the number of corrugated fin units on two sides of a single fin is different, and the edge fin is a straight-edge trapezoidal fin; as shown in fig. 23 (3), the fin has a taper-symmetrical structure, the middle fin of the fin has taper, the number of corrugated fin units on two sides of a single fin is the same, the left and right half sides are symmetrical, and the edge fin is a straight trapezoid fin; as shown in fig. 23 (4), the fin has a taper-shrinking structure, the middle fin of the fin has taper, the number of corrugated fin units on two sides of a single fin is different, the bottom end is shrinking, and the edge fin is a straight-edge trapezoidal fin; as shown in fig. 23 (5), the fin has a taper-outward expansion structure, the middle fin of the fin has taper, the number of corrugated fin units on two sides is different, the bottom end is outward expanded, and the edge fin is a corrugated trapezoidal fin; as shown in fig. 23 (6), the fins have tapered-mirror image corrugated trapezoidal structure, the middle fins of the fins have taper, the structures of two adjacent groups of single fins are mirror images, and the edge fins are corrugated trapezoidal fins.

Claims

1. The parameterized rapid modeling method of the tapered corrugated fin section radiator comprises a fin part and a base plate part, wherein the fin part comprises a middle fin and an edge fin, and the structural characteristic expression of the corrugated fin section radiator is as follows: y=f (Φ (i), Φ (j), Φ (k)); phi (i) in the expression is a functional relation of the middle fin, phi (j) is a functional relation of the substrate part, and phi (k) is a functional relation of the edge fin; the method is characterized in that the construction of the corrugated fin profile radiator model comprises the following steps:

x₁= x₀+R*cosβ,y₁= y₀-R*sinβ；

x₂= x₀+R*cosβ,y₂= y₀+R*sinβ；

x₃= x₀+R*cosβ,y₃= y₀+(r+R)* sinβ+ r*sinβ=y₀+R*sinβ+ 2*r*sinβ;

x₁= x₀-R*cosβ,y₁= y₀-R*sinβ；

x₂= x₀-R*cosβ,y₂= y₀+R*sinβ；

x₃= x₀-R*cosβ,y₃= y₀+(r+R)* sinβ+ r*sinβ=y₀+R*sinβ+ 2*r*sinβ;

x₀'=x₀*cos(α)- y₀*sin(α),y₀'= x₀*sin(α)+ y₀*cos(α)；

x₁'=x₀'+R*cos(β-α),y₁'=y₀'-R*sin(β-α)；

x₂'=x₀'+R*cos(β+α),y₂'=y₀'+R*sin(β+α)；

x₀'=x₀*cos(-α)- y₀*sin(-α),y₀'= x₀*sin(-α)+ y₀*cos(-α);

x₁'=x₀'+R*cos(β+α),y₁'=y₀'-R*sin(β+α)；

x₂'=x₀'+R*cos(β-α),y₂'=y₀'+R*sin(β-α)；

x₀'=x₀*cos(α)- y₀*sin(α),y₀'= x₀*sin(α)+ y₀*cos(α)；

x₁'=x₀'-R*cos(β+α),y₁'=y₀'-R*sin(β+α)；

x₂'=x₀'-R*cos(β-α),y₂'=y₀'+R*sin(β-α)；

x₀'=x₀*cos(-α)- y₀*sin(-α),y₀'= x₀*sin(-α)+ y₀*cos(-α);

x₁'=x₀'-R*cos(β-α),y₁'=y₀'-R*sin(β-α)；

x₂'=x₀'-R*cos(β+α),y₂'=y₀'+R*sin(β+α)；

x₃'=x₀'-(r+R)*cos(β+α)+ r*cos(β-α),y₃'= y₀'+(r+R)* sin(β+α)+ r*sin(β-α);

When n is not an integer, there are three cases:

The first case is that the top is more than half teeth, firstly, a function relation of datum points in a plurality of corrugated fin unit models in the second step and a function relation of O ', A', B 'points and C' in the first step are utilized to establish [ n ] corrugated fin unit models, wherein [ n ] represents that n is the largest integer smaller than n, then, the top is defined for more half teeth, and the top coordinates of the more half teeth are A ^[n]+1'(x₂ ^[n]+1', y₂ ^[n]+1'),A^[n]+1 'coordinates which need to be determined on the basis of the datum points C ^[n]+1'(x₀ ^[n]+1', y₀ ^[n]+1' of [ n ] +1 corrugated fin units;

Wherein x ₀ ^{[n] +1}= x₀,y₀ ^{[n] +1}= y₀+([n]-1)* 2* Pit__ciry;

the second condition is that the bottom is more than half teeth, firstly, a function relation of datum points in the corrugated fin unit models in the second step and a function relation of O ', A ', B ' points and C ' in the first step are utilized to build [ n ] corrugated fin unit models, wherein [ n ] represents that n is the largest integer smaller than n, then, definition is carried out on half teeth with more bottoms, and the bottom coordinates of the half teeth with more bottoms are A ^-1'(x₁ ^-1', y₁ ^-1 ');

The third condition is that the top and the bottom are more than half teeth, namely, the coordinate expressions of the vertex end point A ^[n]+1 'of the top more than half teeth and the bottom end point A ^-1' of the bottom more than half teeth in the multiple corrugated fin unit models are determined by utilizing the functional relation of the two conditions;

When n is not an integer, there are three cases:

x₄=χ__down,y₄=γ__down- L__downfin；

When n is not an integer, there are three cases:

In the first case, χ_ _up is the abscissa x ₂ ^[n]+1 'of the A ^[n]+1'(x₂ ^[n]+1', y₂ ^[n]+1' point of the [ n ] +1 corrugated fin unit for the top half of the teeth;

In the third case, χ_ _up is the abscissa x ₂ ^[n]+1 'of the [ n ] +1th corrugated fin unit A ^[n]+1'(x₂ ^[n]+1', y₂ ^[n]+1') point for more than half teeth at the top and bottom;

x₅=χ__up,y₅= y₄+(H__fin- r__semi)；

x_0λ'= x₀'+Th__fin+R_right*cos(β+α)- R_left*cos(β-α),y_0λ'= y₀'；

wherein R_right and R_left are the radii of curvature of the arcs O ' A ' and O _λ'A_λ ' of the first corrugated fin unit in the right/left half structure, respectively;

x_0λ'= x₀'+Th__fin+ R_left *cos(β+α)- R_right *cos(β-α),y_0λ'= y₀';

x_0λ'= x₀'+Th__fin- R_left *cos(β-α)- R_right *cos(β-α),y_0λ'= y₀';

x_0λ'= x₀'+Th__fin+ R_left *cos(β+α)+ R_right *cos(β+α),y_0λ'= y₀';

The first case is that the number of corrugated fin units of the left and right half structures of a single intermediate fin is equal, namely N is the same, the single intermediate fin phi (i) single is defined as an integral unit, with the single intermediate fin phi (i) single as a reference, pit_ _fin+Th__fin is taken as an offset interval, iteration is carried out according to the number N of the fins, a three-dimensional model of all intermediate fins of the radiator is built, and the functional relationship is as follows:

φ(i)= φ(i)single+N*(Pit__fin+Th__fin)；

a, defining a single intermediate fin phi (i) as an integral unit, taking the single intermediate fin phi (i) as a reference, taking Pit_ _fin+Th__fin as an offset interval, iterating according to the number N of the fins, and establishing a three-dimensional model of all intermediate fins of the radiator;

b, constructing another symmetrical fin phi (i) single_ _reverse by utilizing the constructed single intermediate fin phi (i) single, based on the abscissa x ₄ in the intersection point coordinate H (x ₄,y₄) of the bottom of the single intermediate fin in the step three, which is in contact with the substrate, through the mathematical function relation f { (x ₄+ Th__fin+ Pit__fin/2)+x}=f{(x₄+ Th__fin+ Pit__fin/2) -x }, namely about the axis symmetry of x=x ₄+ Th__fin+ Pit__fin/2, constructing a three-dimensional model of all intermediate fins of the radiator by taking the two fins as an integral unit, taking the two fins as a reference, taking 2 x (Pit_ _fin+Th__fin) as offset intervals, and carrying out iteration according to the number N/2 of the fins, wherein the function relation is as follows:

φ(i)= {φ(i)single, φ(i)single__reverse}+N/2*2*(Pit__fin+Th__fin)；

φ(j) = f (Wid__base, Th__base, L__base)；

offset = {L__base- Th__fin- (N-1)*( Pit__fin+Th__fin)} /2；

x₁₃= x₁₀-Dx__trape,y₁₃= y₁₀+Dy__trape；

2. The parameterized rapid modeling method of a tapered corrugated fin profile radiator according to claim 1, wherein in the first step, for mathematical expressions in two cases of whether or not the taper is provided, the expression in the case of taper can be fully adopted, and if no taper is provided, α=0 is required.