CN109815630B - Design method of high-rigidity square-section beam of frame - Google Patents

Design method of high-rigidity square-section beam of frame Download PDF

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CN109815630B
CN109815630B CN201910140867.XA CN201910140867A CN109815630B CN 109815630 B CN109815630 B CN 109815630B CN 201910140867 A CN201910140867 A CN 201910140867A CN 109815630 B CN109815630 B CN 109815630B
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宋燕利
徐勤超
唐睿杰
华林
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Wuhan University of Technology WUT
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Abstract

A design method of a square section beam with high rigidity of a vehicle frame takes a square section beam with a bamboo-like structure as a design target, firstly, the optimum section width corresponding to the maximum value of the torsional coefficient It of the square section under the conditions of different areas, different bottom thicknesses and different side thicknesses is obtained, then, an optimum section width curve set is drawn according to the optimum section width curve set, the graph set is divided into a plurality of width curve graphs by taking the numerical value of the bottom thickness t1 as a standard, then, the slope of each width curve in the width curve graphs is calculated, the slopes of all the width curves in each width curve graph are averaged to obtain the average slope Kt1 corresponding to the width curve graphs, so that an association table between the Kt1 and the t1 is obtained, and then, the design of the subsequent square section beam is carried out according to the association table to obtain all parameters required by the section of the square section beam with high rigidity. The design can not only design the beam for the frame with light weight and high rigidity, but also has short design time and is very quick.

Description

Design method of high-rigidity square-section beam of frame
Technical Field
The invention relates to a design method of a beam for a frame, belongs to the field of light-weight optimized design of automobiles, and particularly relates to a design method of a high-rigidity square-section beam for a frame.
Background
With the rapid development of the automobile industry, the automobile light weight has become a healthy and continuous development mode pursued by the automobile industry, plays a vital role in reducing oil consumption and emission, and has become a research hotspot in the automobile industry at home and abroad at present. The body frame is an important subject of automobile weight reduction research as a base for supporting and connecting various components of the vehicle. Under actual use conditions, the frame beam deforms to different degrees under the action of self weight and load, so that when the frame beam is designed to be light, the beam needs to have enough strength and rigidity, and the common solution is to increase the elastic modulus of the beam section or adopt better materials, namely, improve the strength of the used materials and increase the area or size of the beam section, but the method undoubtedly increases the weight and cost of the vehicle or occupies more space, so that the methods have limitations. Therefore, a beam for a vehicle frame having light weight and high rigidity and a design process thereof are urgently needed.
The information disclosed in this background section is only for enhancement of understanding of the general background of the patent application and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention aims to overcome the defects and problems that the prior art is difficult to realize the light weight and high rigidity of a beam, and provides a design method of a high-rigidity square section beam of a frame, which can realize the light weight and high rigidity of the beam.
In order to achieve the above purpose, the technical solution of the invention is as follows: a design method of a square section beam with high rigidity of a frame; the square cross-section beam is a hollow cuboid structure, and the cross-section parameters of the square cross-section beam comprise: a represents the width of a square section, t1 represents the bottom thickness of the square section, the thicknesses of the upper bottom and the lower bottom of the square section are consistent, t2 represents the side thickness of the square section, H represents the inner height of the square section, A represents the area of the square section, it represents the torsion resistance coefficient of the square section, wherein the numerical ranges of t1 and t2 are the same, and the numerical range of A is from A1 to An;
the design method comprises the following steps of sequentially obtaining a parameter association table and applying a parameter association table:
the first step, the obtaining process of the parameter association table: firstly according to the following formula
Figure BDA0001978495030000021
By MATLAB simulation, obtaining a variation trend atlas of It along with A, t1 and t2, wherein the variation trend atlas is divided into An A1 sub-atlas, an A2 sub-atlas and An A3 sub-atlas \8230, an 8230and An sub-atlas by taking the numerical value of A as a standard, the A value in each sub-atlas is consistent, and the A1, A2, A3 \82308230andan are arithmetic progression; the single sub-atlas is divided into t11 curve chart, t12 curve chart, t13 curve chart \8230 \ 8230and t1n curve chart with the abscissa of a and the ordinate of It,the t1 values in each graph are consistent, a single graph comprises a t21 curve, a t22 curve and a t23 curve \8230 \ 8230:, a t2n curve, the t2 values on the single curve are consistent, t11, t12 and t13 \8230 \ 8230:, t1n is an arithmetic sequence, t21, t22 and t23 \8230:, 8230, t2n is an arithmetic sequence, the difference value between t11 and t12 is the same as that between t21 and t22, and at the moment, a maximum value of It exists on each curve, and the abscissa corresponding to the maximum value of It is the optimal section width a x Then, according to the maximum value of It in the above-mentioned change trend atlas and its correspondent optimum section width a x Drawing An optimal cross-section width curve set, wherein the optimal cross-section width curve set is divided into a t11 width curve graph, a t12 width curve graph, a t13 width curve graph \8230a \8230at 1n width curve graph by taking the numerical value of t1 as a standard, the ordinate of the width curve graph is t2, the abscissa of the width curve graph is the optimal cross-section width, a single width curve graph comprises An A1 width curve, an A2 width curve and An A3 width curve \8230a8230a, the A values on the single width curve are consistent, then the slope of each width curve is calculated, the average slope of all width curves in each width curve graph is averaged to obtain the average slope Kt1 corresponding to the width curve graph, the average slope Kt1 comprises Kt11, kt12, kt13 8230, 8230a, the Kt1n and corresponds to the t11, t12, t13 \8230andt 1n one by one, so as to obtain An association table between the Kt1 and the t 1;
secondly, the application process of the parameter association table comprises the following steps: firstly, a square section area Ax, a square section bottom thickness t1x and a square section side thickness t2x are determined, ax is in the range from A1 to An, t1x is in the numerical range of t1, t2x is in the numerical range of t2, then the corresponding average slope, namely Kt1x, is selected from the association table according to the selected t1x, and then the formula is adopted
Figure BDA0001978495030000022
Calculating the optimal width a of the cross section x Then according to the formula
Figure BDA0001978495030000023
Calculating the height H in the square section, wherein the bottom thickness t1, the side thickness t2, the inner height H, the width a and the area A of the square section are known, so as to complete the squareThe design of the beam with the shaped cross section.
In the obtaining process of the parameter association table, the calculating the slope of each width curve refers to fitting the curves by using a linear regression equation to obtain the slope corresponding to the curves.
A1, A2 and A3, (8230) \ 8230and An is 1000, 1100, 1200, 1300, 1400 or 1500.
T11, t12, t13 \8230, 8230, t1n is 3, 3.5, 4, 4.5, 5, 5.5, 6.
T21, t22, t23 \8230, 8230, t2n is 3, 3.5, 4, 4.5, 5, 5.5, 6.
The bottom thickness t1 of the square section is different from the side thickness t2 of the square section in value, and the square section is in a non-uniform thickness structure.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention relates to a design method of a high-rigidity square section beam of a vehicle frame, which comprises the steps of firstly taking the square section beam as a design target, then using the biological characteristics of a closed section with unequal thickness of bamboo as a reference, and then utilizing a bionics theory to provide a design process aiming at the square section of the square section beam so as to obtain the bionic square section beam of the vehicle frame, which has light weight, high rigidity, good stability and high material utilization rate, and has the maximum torsional rigidity under the condition of equal mass, thereby simultaneously meeting the requirements of light weight and high rigidity. Therefore, the present invention can achieve both weight reduction and high rigidity of the beam.
2. The invention relates to a design method of a square section beam with high frame rigidity, which comprises the steps of obtaining a parameter association table and an application process of the parameter association table in sequence when a square section is designed, wherein the obtaining process of the parameter association table is utilized to obtain the corresponding relation between the bottom thickness t1 and the average slope Kt1 of the square section so as to establish the association table, and then the association table is applied in the application process of the parameter association table on the basis of the corresponding relation, namely, some known parameters of the square section, such as the area A, the bottom thickness t1 and the side thickness t2, are selected, and then the optimal section width a corresponding to the bottom thickness t1 is determined through the association table x (optimum width of section a) x Corresponding to the maximum square section torsion coefficient ItCorrespondingly) to ensure high stiffness, and then calculating the inner height H to obtain all the parameters of the square section, the advantages of this design method include: firstly, the design of a frame beam with light weight and high rigidity can be realized so as to meet the actual requirement; secondly, in the application after obtaining the association table, all necessary parameters of the square section can be obtained through the clue by determining some known parameters, so that the design of the square section is completed very quickly. Therefore, the design time of the invention is very short, which is beneficial to realizing the rapid design of the beam and shortening the production period.
Drawings
FIG. 1 is a schematic cross-sectional parameter of a square cross-sectional beam according to the present invention.
FIG. 2 shows that A1 is 1000mm 2 And t1 is a graph at 3 mm.
FIG. 3 shows that A1 is 1000mm 2 And t1 is 3.5 mm.
FIG. 4 shows that A1 is 1000mm 2 And t1 is a graph at 4 mm.
FIG. 5 shows A1 as 1000mm 2 And t1 is 4.5 mm.
FIG. 6 shows that A1 is 1000mm 2 And t1 is a graph at 5 mm.
FIG. 7 shows that A1 is 1000mm 2 And t1 is 5.5 mm.
FIG. 8 shows that A1 is 1000mm 2 And t1 is a graph at 6 mm.
FIG. 9 shows that A1 is 1500mm 2 And t1 is a graph at 3 mm.
FIG. 10 shows that A1 is 1500mm 2 And t1 is 3.5 mm.
FIG. 11 shows that A1 is 1500mm 2 And t1 is a graph at 4 mm.
FIG. 12 shows that A1 is 1500mm 2 And t1 is 4.5 mm.
FIG. 13 shows that A1 is 1500mm 2 And t1 is a graph at 5 mm.
FIG. 14 shows that A1 is 1500mm 2 And t1 is 5.5 mm.
FIG. 15 shows that A1 is 1500mm 2 And t1 is a graph at 6 mm.
FIG. 16 is a width graph in which t1 is 3 mm.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description of the invention.
Referring to fig. 1 to 16, a method for designing a high-rigidity square-section beam of a vehicle frame; the square cross-section beam is of a hollow cuboid structure, and the cross-section parameters of the square cross-section beam comprise: a represents the width of a square section, t1 represents the bottom thickness of the square section, the thicknesses of the upper bottom and the lower bottom of the square section are consistent, t2 represents the side thickness of the square section, H represents the inner height of the square section, A represents the area of the square section, it represents the torsion resistance coefficient of the square section, wherein the numerical ranges of t1 and t2 are the same, and the numerical range of A is from A1 to An;
the design method comprises the following steps of sequentially obtaining a parameter association table and applying a parameter association table:
step one, obtaining a parameter association table: firstly according to the following formula
Figure BDA0001978495030000041
By MATLAB simulation, obtaining a variation trend atlas of It along with A, t1 and t2, wherein the variation trend atlas is divided into An A1 sub-atlas, an A2 sub-atlas and An A3 sub-atlas \8230, an 8230and An sub-atlas by taking the numerical value of A as a standard, the A value in each sub-atlas is consistent, and the A1, A2, A3 \82308230andan are arithmetic progression; a single sub-graph set is divided into a t11 graph, a t12 graph and a t13 graph in which t1 values are consistent, a t11 graph, a t12 graph and a t13 graph in which the abscissa of the graph is a and the ordinate of the graph is It, a t21 graph, a t22 graph and a t23 graph in which t1 values are consistent, a t 8230, a t 8230and a t2n graph in which t2 values are consistent, a t11 graph, a t12 graph and a t13 graph in which t 8230are included, a t1n is an arithmetic difference sequence, a t21 graph, a t22 graph, a t23, a 8230and a t2n is an arithmetic difference sequence, and the difference values of the t11 and the t12 are the same as those of the t21 and the t22 graphs, wherein the maximum value of the It exists on each graph, and the abscissa corresponding to the maximum value of the It is the optimal section width a x According to It in the above-mentioned trend graph setMaximum value and its corresponding optimum cross-sectional width a x Drawing An optimal cross-section width curve set, wherein the optimal cross-section width curve set is divided into a t11 width curve graph, a t12 width curve graph, a t13 width curve graph \8230a \8230at 1n width curve graph by taking the numerical value of t1 as a standard, the ordinate of the width curve graph is t2, the abscissa of the width curve graph is the optimal cross-section width, a single width curve graph comprises An A1 width curve, an A2 width curve and An A3 width curve \8230a8230a, the A values on the single width curve are consistent, then the slope of each width curve is calculated, the average slope of all width curves in each width curve graph is averaged to obtain the average slope Kt1 corresponding to the width curve graph, the average slope Kt1 comprises Kt11, kt12, kt13 8230, 8230a, the Kt1n and corresponds to the t11, t12, t13 \8230andt 1n one by one, so as to obtain An association table between the Kt1 and the t 1;
secondly, the application process of the parameter association table comprises the following steps: firstly, a square section area Ax, a square section bottom thickness t1x and a square section side thickness t2x are determined, ax is in the range from A1 to An, t1x is in the numerical range of t1, t2x is in the numerical range of t2, then the corresponding average slope, namely Kt1x, is selected from the association table according to the selected t1x, and then the formula is adopted
Figure BDA0001978495030000051
Calculating the optimal width a of the cross section x Then according to the formula
Figure BDA0001978495030000052
And calculating the inner height H of the square section, wherein the bottom thickness t1, the side thickness t2, the inner height H, the width a and the area A of the square section are known, and the design of the square section beam can be completed.
In the obtaining process of the parameter association table, the calculating the slope of each width curve refers to fitting the curves by using a linear regression equation to obtain the slopes corresponding to the curves.
A1, A2 and A3 \8230, wherein An is 1000, 1100, 1200, 1300, 1400 or 1500.
T11, t12, t13 \8230, 8230, t1n is 3, 3.5, 4, 4.5, 5, 5.5, 6.
T21, t22, t23 \8230, 8230, t2n is 3, 3.5, 4, 4.5, 5, 5.5, 6.
The bottom thickness t1 of the square section is different from the side thickness t2 of the square section in value, and the square section is in a non-uniform thickness structure.
The principle of the invention is illustrated as follows:
in nature, bamboo is a typical high-efficiency light biological structure, and has the characteristics of high rigidity, high strength and the like, wherein the density of the bamboo is about one tenth of that of steel, but the specific rigidity of the bamboo is 2-5 times that of the steel. In addition, the bamboo has a slenderness ratio of 1/160 to 1/260, which is difficult to achieve with conventional structures. The bamboo has the most obvious structural characteristics that the hollow closed section with different thicknesses has important contribution significance to high rigidity and high strength performance. The invention relates to a method for designing a high-rigidity square-section beam of a vehicle frame, which is characterized in that the biological structure tissue of bamboo is analyzed by using the thinking of bionic design, and the advantages of the bamboo are used for reference and application to the design of the vehicle frame beam. In the present invention, n is a natural number.
Example 1:
referring to fig. 1, fig. 1 is a schematic diagram of cross-sectional parameters of a square cross-sectional beam, and design parameters required for patterning thereof include: a represents the square cross-sectional width, t1 represents the square cross-sectional bottom thickness, the square cross-sectional upper and lower bottom thicknesses are the same, t2 represents the square cross-sectional side thickness, and H represents the square cross-sectional inner height.
In example 1, the numerical ranges of t1 and t2 for the light truck type were 3, 3.5, 4, 4.5, 5, 5.5, and 6 (in mm), and the numerical range of a was 1000, 1100, 1200, 1300, 1400, and 1500 (in mm) 2 )。
The first step, the obtaining process of the parameter association table: firstly according to the following formula
Figure BDA0001978495030000061
By MATLAB simulation, we obtain a trend chart of It with a, t1, and t2, which is divided into a =1000 sub-chart set, a =1100 sub-chart set, a =1200 sub-chart set, a =1300 sub-chart set, a =1400 sub-chart set, and a =1500 sub-chart set based on the value of a, and fig. 2-8 show a =1000 sub-chart set, and fig. 3-15 show a =1500 sub-chart set.
Referring to fig. 2-8, a =1000 sub-graph set is divided into a t1=3 graph, a t1=3.5 graph, a t1=4 graph, a t1=4.5 graph, a t1=5 graph, a t1=5.5 graph, and a t1=6 graph by using a value of t1 as a standard, a of all graphs is 1000, and a t2=3 graph, a t2=3.5 graph, a t2=4 graph, a t2=4.5 graph, a t2=5 graph, a t2=5.5 graph, and a t2=6 graph are respectively plotted by using a value of t2 as a standard in each graph.
Referring to fig. 3-fig. 15, a =1500 sub-plot set is also divided into a t1=3 plot, a t1=3.5 plot, a t1=4 plot, a t1=4.5 plot, a t1=5 plot, a t1=5.5 plot, and a t1=6 plot, using the value of t1 as a standard, a of all the plots is 1500, and a t2=3 plot, a t2=3.5 plot, a t2=4 plot, a t2=4.5 plot, a t2=5 plot, a t2=5.5 plot, and a t2=6 plot are plotted using the value of t2 as a standard in each plot, respectively.
The a =1100 sub-map set, the a =1200 sub-map set, the a =1300 sub-map set, and the a =1400 sub-map set are consistent with the a =1000 sub-map set and the a =1500 sub-map set drawing method described above.
As is evident from all the graphs above, there is a maximum value of It on each graph, and the abscissa corresponding to the maximum value of It is the optimum section width a x At this time, the maximum value of It in the above-mentioned trend chart set and its corresponding optimum section width a are further used x Drawing an optimal section width curve set which is divided into a t1=3 width curve, a t1=3.5 width curve, a t1=4 width curve, a t1=4.5 width curve, a t1=5 width curve, a t1=5.5 width curve and a t1=6 width curve by taking the numerical value of t1 as a standard.
Taking a width curve of t1=3 as an example, referring to fig. 16, the ordinate in the figure is t2, and the abscissa is the optimal section widtha x The individual width profiles include a =1000 width curve, a =1100 width curve, a =1200 width curve, a =1300 width curve, a =1400 width curve, a =1500 width curve, and then the slopes of the respective curves are found as follows:
Figure BDA0001978495030000071
then, the slope in the table above is averaged to obtain the average slope Kt1= -4.564 corresponding to the t1=3 width curve graph, and the average slope Kt1 corresponding to the other bottom thicknesses t1 is calculated by the same method, and finally the correlation table is obtained as follows:
Figure BDA0001978495030000072
secondly, the application process of the parameter association table comprises the following steps: selecting a square section area A =1300, a bottom thickness t1=4 and a side thickness t2=3, checking the average slope Kt1 corresponding to t1=4 to be-3.3974 according to the association table, and then calculating the average slope according to the formula
Figure BDA0001978495030000073
Calculating the optimal width a of the cross section x Is 88.7, and is based on the formula
Figure BDA0001978495030000074
The inner height H of the square cross section was calculated to be 98.4, and in this case, the bottom thickness t1=4mm, the side thickness t2=3mm, the inner height H =98.4mm, the width a =88.7mm, and the area a =1300mm of the square cross section 2 The design of the square section beam can be completed after the beam is known, and the design of the square section under the other known data can be performed by analogy, so that the design is very quick.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.

Claims (6)

1. A design method of a high-rigidity square-section beam of a vehicle frame is characterized by comprising the following steps: the square cross-section beam is a hollow cuboid structure, and the cross-section parameters of the square cross-section beam comprise: a represents the width of a square section, t1 represents the bottom thickness of the square section, the thicknesses of the upper bottom and the lower bottom of the square section are consistent, t2 represents the side thickness of the square section, H represents the inner height of the square section, A represents the area of the square section, it represents the torsion resistance coefficient of the square section, wherein the numerical ranges of t1 and t2 are the same, and the numerical range of A is from A1 to An;
the design method comprises the following steps of sequentially obtaining a parameter association table and applying a parameter association table:
step one, obtaining a parameter association table: firstly according to the following formula
Figure FDA0001978495020000013
ω=(H+t 1 )×(a-t 2 ),
Figure FDA0001978495020000012
By MATLAB simulation, obtaining a variation trend atlas of It along with A, t1 and t2, wherein the variation trend atlas is divided into An A1 sub-atlas, an A2 sub-atlas and An A3 sub-atlas \8230, an 8230and An sub-atlas by taking the numerical value of A as a standard, the A value in each sub-atlas is consistent, and the A1, A2, A3 \82308230andan are arithmetic progression; a single sub-graph set is divided into a t11 graph, a t12 graph, a t13 graph, a 8230, a 82303030and a t1n graph by taking the numerical value of t1 as a standard, the abscissa of the graph is a, the ordinate of the graph is It, the t1 values in each graph are consistent, the single graph comprises a t21 graph, a t22 graph, a t23 graph, a 8230and a t 823030in each graph, the t2 values on the single graph are consistent, the t11, the t12, the t13 8230, the 8230and the t1n are arithmetic difference number series, the t21, the t22, the t23, the 8230and the t2n are arithmetic number series, the difference values of the t11 and the t12 are the same as the difference values of the t21 and the t22, and at the moment, a maximum value of the It exists on each graph, and the abscissa corresponding to the maximum value of the It is the optimal section width a x Then, according to the maximum value of It in the above-mentioned change trend atlas and its correspondent maximum valueOptimum cross-sectional width a x Drawing an optimal section width curve set which is divided into a t11 width curve graph, a t12 width curve graph, a t13 width curve graph (8230); 8230; and a t1n width curve graph by taking the numerical value of t1 as a standard, wherein the ordinate of the width curve graph is t2, and the abscissa thereof is the optimal section width a x The method comprises the steps that a single width curve graph comprises An A1 width curve, an A2 width curve and An A3 width curve \8230, an 8230and An width curve, the A values on the single width curve are consistent, then the slope of each width curve is calculated, and the slopes of all the width curves in each width curve graph are averaged to obtain An average slope Kt1 corresponding to the width curve graph, wherein the average slope Kt1 comprises Kt11, kt12, kt13 \8230, an 8230, a Kt1n and t11, t12, t13 \8230, an \8230anda t1n are in one-to-one correspondence, so that An association table between the Kt1 and the t1 is obtained;
step two, the application process of the parameter association table comprises the following steps: firstly, a square section area Ax, a square section bottom thickness t1x and a square section side thickness t2x are determined, ax is in the range from A1 to An, t1x is in the numerical range of t1, t2x is in the numerical range of t2, then the corresponding average slope, namely Kt1x, is selected from the association table according to the selected t1x, and then the formula is adopted
Figure FDA0001978495020000021
Calculating the optimal width a of the cross section x Then according to the formula
Figure FDA0001978495020000022
And (3) calculating the inner height H of the square section, wherein the bottom thickness t1, the side thickness t2, the inner height H, the width a and the area A of the square section are known, and then the design of the square section beam can be completed.
2. The design method of the square cross-section beam with high rigidity of the frame according to claim 1, characterized in that: in the obtaining process of the parameter association table, the calculating the slope of each width curve refers to fitting the curves by using a linear regression equation to obtain the slope corresponding to the curves.
3. The method for designing the square cross-section beam with the high rigidity for the vehicle frame according to claim 1 or 2, is characterized in that: a1, A2 and A3, (8230) \ 8230and An is 1000, 1100, 1200, 1300, 1400 or 1500.
4. The method for designing the square cross-section beam with the high rigidity for the vehicle frame according to claim 1 or 2, is characterized in that: t11, t12, t13 \8230, 8230, t1n is 3, 3.5, 4, 4.5, 5, 5.5, 6.
5. The method for designing the square cross-section beam with high rigidity for the vehicle frame according to claim 1 or 2, is characterized in that: t21, t22, t23 \8230, 8230, t2n is 3, 3.5, 4, 4.5, 5, 5.5, 6.
6. The method for designing the square cross-section beam with the high rigidity for the vehicle frame according to claim 1 or 2, is characterized in that: the bottom thickness t1 of the square section is different from the side thickness t2 of the square section in value, and the square section is in a non-uniform thickness structure.
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