CN106934175B - Negative poisson ratio structure energy-absorbing box and multi-objective optimization method thereof - Google Patents
Negative poisson ratio structure energy-absorbing box and multi-objective optimization method thereof Download PDFInfo
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Abstract
The invention discloses a negative poisson ratio structure energy-absorbing box and a multi-objective optimization method thereof, wherein the negative poisson ratio structure energy-absorbing box consists of an energy-absorbing box body (1), a front mounting plate (2), a rear mounting plate (5) and a three-dimensional negative poisson ratio structure inner core (3). Because the three-dimensional negative poisson ratio structure inner core is composed of a large number of negative poisson ratio unit cell structures, parameters of the negative poisson ratio unit cell structures have great influence on energy absorption performance of the energy absorption box, the invention provides a multi-objective optimization method based on the negative poisson ratio structure energy absorption box, the parameters of part of the negative poisson ratio unit cell structures are used as optimization variables, objective functions are established, constraint conditions are set, an energy absorption box optimization model of the negative poisson ratio structure is established, and the multi-objective optimization is carried out on the energy absorption box of the negative poisson ratio structure by adopting a multi-objective particle swarm optimization algorithm.
Description
Technical Field
The invention belongs to the field of passive safety protection of automobiles, and particularly relates to a negative poisson ratio structure energy-absorbing box and a multi-objective optimization method thereof.
Background
When an automobile collides with the front surface, the compression deformation of the front energy absorption box of the automobile is mainly used for absorbing collision energy as much as possible, reducing acceleration generated by collision and reducing the maximum collision force so as to alleviate the impact, thereby reducing the collision injury to passengers and reducing the maintenance cost of the automobile. One end of the energy absorption box is connected to the longitudinal beam, and the other end of the energy absorption box is connected with a bumper beam at the front end of the vehicle. At present, the appearance of a common energy-absorbing box is of a square structure, and the structure can achieve a certain energy-absorbing effect, but the deformation is not stable enough and the compression is not thorough enough when in collision, so that the energy cannot be absorbed and decomposed to the greatest extent, partial energy is transmitted to a longitudinal beam connected with the energy-absorbing box along the axial direction, the bending damage of the longitudinal beam is caused, the damage of parts in an engine cabin is further caused, and even the energy is transmitted to the safety of passengers in critical vehicles in the passenger cabin.
The negative poisson ratio structural material can generate stable and controllable compression deformation when being subjected to load, so that the negative poisson ratio structural material shows more excellent performance in the aspect of energy absorption, and the negative poisson ratio structural material is filled in the shell of the common energy-absorbing box to form the energy-absorbing box with the negative poisson ratio structure, so that the problem of insufficient collision energy absorption caused by insufficient deformation and insufficient compression of the common energy-absorbing box when a vehicle collides can be well solved.
The energy absorption performance of the energy-absorbing box with the negative poisson ratio structure is closely related to the parameters of the negative poisson ratio unit cell structure, and the energy absorption performance of the energy-absorbing box formed by the unit cell structures with different geometric parameters is also different, so that the energy-absorbing box with the negative poisson ratio unit cell structure needs to be optimally designed to achieve the aim of further improving the energy-absorbing effect of the energy-absorbing box.
Disclosure of Invention
The invention aims to overcome the defects of the background technology and provides a negative poisson ratio structure energy absorption box and a multi-objective optimization method thereof.
The invention solves the technical problems by the following technical proposal:
the negative poisson ratio unit cell structure comprises two symmetrically parallel bottom edges, wherein the same sides of the two bottom edges are connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, and t is more than or equal to 0.6mm and less than or equal to 1.2mm; the widths of the first bevel edge, the second bevel edge and the bottom edge are b, and b is more than or equal to 2.2mm and less than or equal to 3mm; the included angle between each bevel edge and the adjacent bottom edge is d, and d is more than or equal to 55 degrees and less than or equal to 75 degrees; the length of the two bottom edges is a, and a is more than or equal to 12mm and less than or equal to 16mm; the vertical distance between the two bottom edges is h, and h is more than or equal to 8mm and less than or equal to 13mm.
Further, the thickness t of the first oblique side, the second oblique side and the bottom side is 1.18mm; the width b of the first bevel edge, the second bevel edge and the bottom edge is 2.98mm; the included angle d between each bevel edge and the adjacent bottom edge is 56.1 degrees; the length a of the two bottom edges is 14.71mm; the vertical distance h between the two bottom edges is 8mm.
The three-dimensional negative poisson ratio structure inner core based on the negative poisson ratio unit structure comprises more than one foundation unit, wherein the foundation unit comprises two negative poisson ratio unit structures, the bottom edges of the two negative poisson ratio unit structures are mutually orthogonal, the foundation units are arranged in an array along the extending directions of the two ends of the vertical distance h between the two bottom edges, and the foundation units are arranged in an array along the extending directions of the two ends of the length a of the two bottom edges.
The energy-absorbing box with the negative poisson ratio structure comprises an energy-absorbing box body (1), a front mounting plate (2) and a rear mounting plate (5), wherein one end of the energy-absorbing box body (1) is connected with the front mounting plate (2), and the other end of the energy-absorbing box body (1) is connected with the rear mounting plate (5); the front mounting plate (2) is used for being connected with the automobile bumper beam through bolts, and the rear mounting plate (5) is used for being connected with the longitudinal beam of the automobile body through bolts.
Further, the energy-absorbing box body (1) is of a hollow prismatic structure with an octagonal section, the whole surface of the energy-absorbing box body (1) comprises an upper surface, a lower surface, a left side surface, a right side surface and inclined side surfaces, the upper surface is symmetrically parallel to the lower surface, the left side surface is symmetrically parallel to the right side surface, the left side surface is perpendicular to the upper surface, the number of the inclined side surfaces is four, and the inclined side surfaces are respectively positioned between the upper surface and the right side surface, between the right side surface and the lower surface, between the lower surface and the left side surface, and between the left side surface and the upper surface;
three first induction grooves (41) are symmetrically arranged on the left side surface and the right side surface, and the first induction grooves (41) are positioned at the quarter points of the axial length of the energy absorption box body (1); the upper surface is provided with two induction grooves II (42), the lower surface is provided with two induction grooves III, the induction grooves II (42) and the induction grooves III are mutually symmetrical, the induction grooves II (42) are positioned in the middle of the projection positions of the upper surfaces of the adjacent two induction grooves I (41), and the induction grooves III are positioned in the middle of the projection positions of the lower surfaces of the adjacent two induction grooves I (41); the second induction groove (42) and the first induction groove (41) are concave, the third induction groove is convex, and the depths of the first induction groove (41), the second induction groove (42) and the third induction groove are the same.
The multi-objective optimization method of the negative poisson ratio structure energy-absorbing box comprises the steps that a three-dimensional negative poisson ratio structure inner core based on a negative poisson ratio unit cell structure is arranged in the negative poisson ratio structure energy-absorbing box, the negative poisson ratio unit cell structure comprises two symmetrically parallel bottom edges, the same sides of the two bottom edges are connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, the widths of the first inclined edge, the second inclined edge and the bottom edge are b, the included angle between each inclined edge and the adjacent bottom edge is d, the lengths of the two bottom edges are a, and the vertical distance between the two bottom edges is h; the three-dimensional negative poisson ratio structure inner core comprises more than one basic unit, the basic unit comprises two negative poisson ratio unit structures, the bottom edges of the two negative poisson ratio unit structures are mutually orthogonal, the basic units are arranged in an array along the extending directions of the two ends of the vertical distance h between the two bottom edges, and the basic units are arranged in an array along the extending directions of the two ends of the length a of the two bottom edges, and the multi-objective optimization method of the negative poisson ratio structure energy absorption box comprises the following steps:
step 1), in ISIGHT optimization software, an optimal Latin hypercube design method is selected, N groups of design sample points are uniformly selected within a threshold range preset by each design variable parameter, the design variable parameters are respectively the length a of the bottom edge of a negative Poisson ratio unit cell structure, the included angle d of each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative Poisson ratio unit cell structure and the width b of the negative Poisson ratio unit cell structure, and N is a natural number larger than 0; the preset thresholds of the design variable parameters are respectively as follows: a=14mm, b=2.6mm, h=10.5mm, d=65°, t=0.9 mm; the change ranges of the preset threshold values are respectively as follows: a epsilon [12,16], b epsilon [2.2,3], h epsilon [8,13], d epsilon [55 DEG, 75 DEG ], t epsilon [0.6,1.2];
step 2), establishing CAD models of N groups of inner cores of the three-dimensional negative poisson ratio structures in CATIA software according to the selected design sample points;
the CAD model forming method of the three-dimensional negative poisson ratio structure inner core comprises the following detailed steps: according to the generated design sample points, a negative poisson ratio unit cell structure model is built in CATIA software; then, carrying out array change in the X-axis direction on the negative Poisson ratio unit cell structure model; then, replication change rotated by 90 degrees around the X axis is carried out; finally, performing array replication changes in the Y-axis direction and the Z-axis direction to form the inner core of the three-dimensional negative poisson ratio structure;
step 3), importing a CAD model of the inner core of the three-dimensional negative poisson ratio structure into HYPERMESH software, performing geometric cleaning and grid division on the CAD model, and setting the material and thickness of the inner core of the three-dimensional negative poisson ratio structure;
step 4), a traditional energy-absorbing box shell model without a three-dimensional negative poisson ratio structure inner core and a rigid wall model for testing collision are led into HYPERMESH, the three-dimensional negative poisson ratio structure inner core is filled in the traditional energy-absorbing box shell, the collision speed between the rigid wall and the energy-absorbing box with the negative poisson ratio structure is set, 6 degrees of freedom of a node which is not contacted with the rigid wall when the energy-absorbing box with the negative poisson ratio structure collides are restrained, and meanwhile contact and output between the rigid wall and the energy-absorbing box with the negative poisson ratio structure are defined;
step 5), calculating peak collision force P, average collision force F, compression displacement S and mass m of the energy-absorbing box with the negative Poisson ratio structure during collision according to the simulation output result;
step 6), selecting an order of a high-order response surface model, taking a bottom edge length a, an included angle d between a bevel edge and the bottom edge, a vertical distance h between the two bottom edges, a thickness t of the negative poisson ratio unit cell structure and a width b of the negative poisson ratio unit cell structure corresponding to N groups of negative poisson ratio unit cell structures as inputs, and taking a peak collision force P, an average collision force F, a compression displacement S and a mass m of an energy absorption box corresponding to N groups of negative poisson ratio unit cell structures as outputs to construct the following four response surface models: the mass m response surface model, the compression displacement S response surface model, the average collision force F response surface model and the peak collision force P response surface model of the negative poisson ratio structure energy-absorbing box;
step 7), calculating correlation coefficients R of the four response surface model fits respectively 2 And a root mean square error RMSE;
step 8), for each response surface model, the correlation coefficient R thereof is calculated 2 The Root Mean Square Error (RMSE) is respectively compared with a preset first threshold value and a preset second threshold value; if the correlation coefficient R of four response surface models 2 Step 9) is executed when the first threshold value is equal to or greater than a preset first threshold value and the Root Mean Square Error (RMSE) is equal to or less than a preset second threshold value; otherwise, re-executing the steps 1) to 7) until the correlation coefficients R of the four response surface models 2 Are all greater than or equal to a preset first threshold valueThe Root Mean Square Error (RMSE) and the Root Mean Square Error (RMSE) are respectively smaller than or equal to a preset second threshold value of 0.08;
step 9), taking the mass m and the compression displacement S of the energy-absorbing box with the negative poisson ratio structure as optimization targets, taking the peak collision force P, the average collision force F, the compression displacement S and the mass m as system constraint conditions, and taking the bottom edge length a of the energy-absorbing box with the negative poisson ratio structure, the included angle d of each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the energy-absorbing box with the negative poisson ratio and the width b of the energy-absorbing box with the negative poisson ratio as design variables to establish a mathematical model for optimizing the energy-absorbing box with the negative poisson ratio;
step 10), optimizing the bottom edge length a of the negative poisson ratio unit cell structure, the included angle d between each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative poisson ratio unit cell structure and the width b of the negative poisson ratio unit cell structure in Isight software by adopting a multi-target particle swarm optimization algorithm according to the established optimized mathematical model to obtain a Pareto solution set, and selecting a group of optimal solutions from the Pareto solution set;
and 11) establishing a negative poisson ratio structure energy-absorbing box simulation model according to the optimized optimal solution, and carrying out solving calculation in LS-DYNA software to obtain an actual simulation result of the optimized negative poisson ratio structure energy-absorbing box.
Further, the mass of the rigid wall in the step 4) is 900kg, and the collision speed between the rigid wall and the negative poisson ratio structure energy absorption box is 15km/h.
Further, the order of the high-order response surface model in step 6) is second order, which is generally expressed as:
wherein m is the number of design parameters, x i And x j For input, y is the original response, a i 、a ii And a ij All are undetermined coefficients, the number of which is k and:
further, the mass response surface model, the compression displacement response surface model, the average collision force response surface model and the peak collision force response surface model of the negative poisson ratio structure energy absorption box in the step 6) are respectively as follows:
1) The response surface model of the negative poisson ratio structure energy absorption box mass m is as follows:
m＝3.408-0.2187a+0.3961b+0.0855h-0.0426d+0.957t+0.0052a 2 -0.0146b 2 -0.0000576h 2 +0.000176d 2 -0.022t 2 -0.0139ab-0.00272ah+0.00198ad-0.0313at-0.00094bh-0.00123bd+0.0864bt-0.000666hd-0.0055ht-0.00462dt
2) The response surface model of the negative poisson ratio structure energy absorption box compression displacement S is as follows:
S＝18.3507+6.4761a-3.9816b+2.2986h+1.2399d-28.604t-0.1569a 2 -2.3859b 2 -0.0877h 2 -0.00696d 2 +0.644t 2 +0.7614ab-0.1554ah-0.02834ad+1.546at+0.2692bh+0.07567bd-8.2472bt+0.0125hd+1.0947ht-0.1047dt
3) The response surface model of the average collision force F of the energy absorption box with the negative poisson ratio structure is as follows:
F＝135.9968-4.3789a+0.5376b-1.417h-1.0003d+21.253t+0.1228a 2 +2.3099b 2 +0.0478h 2 +0.0062d 2 +3.397t 2 -0.6732ab+0.1196ah+0.0206ad-1.2859at-0.2522bh-0.05623bd+7.818bt-0.0037hd-1.0269ht-0.02654dt
4) The response surface model of the negative poisson ratio structure energy absorption box peak collision force P is as follows:
P＝129.4295-3.4271a-0.0704b-2.6319h-0.5749d+116.2096t+0.2734a 2 +3.369b 2 +0.1481h 2 +0.0042d 2 +14.5422t 2 -1.1753ab+0.1665ah-0.0061ad-6.025at-0.3413bh+0.1725bd-2.6305bt-0.0196hd-1.6835ht-0.0027dt。
further, the mathematical model for optimizing the negative poisson ratio structural energy absorption box in the step 9) is as follows:
the beneficial effects of the invention are as follows:
1. according to the invention, the three-dimensional inner core with the negative poisson ratio structure is filled in the traditional energy-absorbing box to form the energy-absorbing box with the negative poisson ratio structure, so that the defects of unstable deformation, poor energy-absorbing effect and the like of the traditional energy-absorbing box when a vehicle collides are effectively solved.
2. After the parameters of the negative poisson ratio unit cell structure are optimized by adopting a multi-target particle swarm optimization algorithm, the energy absorption performance of the negative poisson ratio structure energy absorption box is further improved.
Drawings
FIG. 1 is a schematic diagram of a negative poisson's ratio structural crash box of the present invention;
FIG. 2 is a schematic diagram of a CAD model of the inner core of the three-dimensional negative Poisson's ratio structure of the present invention;
FIG. 3 is a schematic diagram of a negative Poisson's ratio cell structure;
FIG. 4 is a flow chart of a multi-objective optimization method of the negative poisson's ratio structure energy-absorbing box of the invention;
FIG. 5 is a flow chart of a multi-objective particle swarm optimization algorithm according to the present invention;
FIG. 6 is a schematic diagram of the crash results of a negative poisson's ratio structural crash box of the present invention.
Reference numerals illustrate:
the energy-absorbing box comprises a 1-energy-absorbing box body, a 2-front mounting plate, a 3-three-dimensional inner core with a negative poisson ratio structure, a 41-induction groove I, a 42-induction groove II and a 5-rear mounting plate.
Detailed Description
The invention is further illustrated by the following examples, which are intended to be illustrative only and not limiting in any way.
It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The negative poisson ratio unit cell structure comprises two symmetrically parallel bottom edges, wherein the same sides of the two bottom edges are connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards. The thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, and t is more than or equal to 0.6mm and less than or equal to 1.2mm; the widths of the first bevel edge, the second bevel edge and the bottom edge are b, and b is more than or equal to 2.2mm and less than or equal to 3mm; the included angle between each bevel edge and the adjacent bottom edge is d, and d is more than or equal to 55 degrees and less than or equal to 75 degrees; the length of the two bottom edges is a, and a is more than or equal to 12mm and less than or equal to 16mm; the vertical distance between the two bottom edges is h, and h is more than or equal to 8mm and less than or equal to 13mm.
These 5 parameters determine the overall characteristics of the negative poisson's ratio cell structure, as well as its dimensional change. The negative poisson ratio unit cell structure is in an inward concave hexagonal honeycomb structure, and when the negative poisson ratio unit cell structure is subjected to uniaxial compression, the inclined side of the structure is bent and deformed so as to generate a negative poisson ratio effect.
The thickness t of the first oblique side, the second oblique side and the bottom side of the negative poisson ratio unit cell structure is 1.18mm; the width b of the first bevel edge, the second bevel edge and the bottom edge is 2.98mm; the included angle d between each bevel edge and the adjacent bottom edge is 56.1 degrees; the length a of the two bottom edges is 14.71mm; the vertical distance h between the two bottom edges is 8mm.
The three-dimensional negative poisson ratio structure inner core based on the negative poisson ratio unit structure comprises more than one foundation unit, wherein the foundation unit comprises two negative poisson ratio unit structures, the bottom edges of the two negative poisson ratio unit structures are mutually orthogonal, the foundation units are arranged in an array along the extending directions of the two ends of the vertical distance h between the two bottom edges, and the foundation units are arranged in an array along the extending directions of the two ends of the length a of the two bottom edges. The whole three-dimensional negative poisson ratio structure inner core 3 is designed into a square energy absorption carrier consisting of 22 x 9 x 4 = 792 negative poisson ratio unit cell structures.
The energy-absorbing box with the negative poisson ratio structure is internally provided with the inner core with the three-dimensional negative poisson ratio structure, and the inner core with the three-dimensional negative poisson ratio structure has the characteristics of more stable deformation and more sufficient compression when being subjected to the load, so that the energy absorption performance of the energy-absorbing box is well improved. The energy-absorbing box with the negative poisson ratio structure comprises an energy-absorbing box body 1, a front mounting plate 2 and a rear mounting plate 5, wherein one end of the energy-absorbing box body 1 is connected with the front mounting plate 2, and the other end of the energy-absorbing box body 1 is connected with the rear mounting plate 5; the front mounting plate 2 is used for being connected with a car bumper beam through 2 bolts, and the rear mounting plate 5 is used for being connected with a longitudinal beam of a car body through 4 bolts.
The energy-absorbing box body 1 is of a hollow prismatic structure with an octagonal section, and the whole surface of the energy-absorbing box body 1 comprises an upper surface, a lower surface, a left side surface, a right side surface and an inclined side surface. The upper surface is symmetrically parallel to the lower surface, the left side surface is symmetrically parallel to the right side surface, and the left side surface is perpendicular to the upper surface. The inclined side surfaces are respectively positioned between the upper surface and the right side surface, between the right side surface and the lower surface, between the lower surface and the left side surface and between the left side surface and the upper surface.
Three first guiding grooves 41 are symmetrically arranged on the left side face and the right side face, and the first guiding grooves 41 are positioned at four equally dividing points of the axial length of the energy absorption box body 1; the upper surface is provided with two guiding grooves II 42, the lower surface is provided with two guiding grooves III, the guiding grooves II 42 and the guiding grooves III are mutually symmetrical, the guiding grooves II 42 are positioned in the middle of the projection positions of the upper surfaces of the adjacent guiding grooves I41, and the guiding grooves III are positioned in the middle of the projection positions of the lower surfaces of the adjacent guiding grooves I41; the second guiding groove 42 and the first guiding groove 41 are concave, the third guiding groove is convex, and the depth of the first guiding groove 41, the second guiding groove 42 and the third guiding groove is the same. The induced groove can guide the energy-absorbing box to deform in a design mode, so that the energy-absorbing box deforms stably and sufficiently when collision occurs, and the energy-absorbing performance of the energy-absorbing box is improved.
The invention also discloses a multi-objective optimization method of the negative poisson ratio structure energy-absorbing box, wherein a three-dimensional negative poisson ratio structure inner core based on a negative poisson ratio unit cell structure is arranged in the negative poisson ratio structure energy-absorbing box, the negative poisson ratio unit cell structure comprises two bottom edges which are symmetrically parallel, the same sides of the two bottom edges are connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, the widths of the first inclined edge, the second inclined edge and the bottom edge are b, the included angle between each inclined edge and the adjacent bottom edge is d, the lengths of the two bottom edges are a, and the vertical distance between the two bottom edges is h; the three-dimensional negative poisson ratio structure inner core comprises more than one foundation unit, the foundation unit comprises two negative poisson ratio unit structures, the bottom edges of the two negative poisson ratio unit structures are mutually orthogonal, the foundation units are arrayed along the extending directions of the two ends of the vertical distance h between the two bottom edges, and the foundation units are arrayed along the extending directions of the two ends of the length a of the two bottom edges, and the multi-objective optimization method of the negative poisson ratio structure energy absorption box comprises the following steps:
step 1), in ISIGHT optimization software, an optimal Latin hypercube design method is selected, N groups of design sample points are uniformly selected within a threshold range preset by each design variable parameter, the design variable parameters are respectively the length a of the bottom edge of a negative Poisson ratio unit cell structure, the included angle d of each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative Poisson ratio unit cell structure and the width b of the negative Poisson ratio unit cell structure, and N is a natural number larger than 0; the preset thresholds of the design variable parameters are respectively as follows: a=14mm, b=2.6mm, h=10.5mm, d=65°, t=0.9 mm; the change ranges of the preset threshold values are respectively as follows: a epsilon [12,16], b epsilon [2.2,3], h epsilon [8,13], d epsilon [55 DEG, 75 DEG ], t epsilon [0.6,1.2].
Step 2), establishing a CAD model of an inner core of the 80-group three-dimensional negative poisson ratio structure in CATIA software according to the selected design sample points, wherein the detailed modeling step of the model is shown in figure 2;
the method for forming the CAD model of the inner core of the three-dimensional negative poisson ratio structure comprises the following detailed steps:
step 2.1) establishing a negative poisson ratio unit cell structure model in CATIA software according to the generated design sample points, as shown in Step1 in fig. 2;
step 2.2) then performing an array change in the X-axis direction on the unit cell structure model, as shown in Step2 in FIG. 2;
step 2.3) then performs a replication change rotated 90 ° about the X-axis, as shown in Step3 in fig. 2;
step 2.4) continuing the array change in the Y-axis direction, as shown in Step4 of fig. 2;
step 2.5) finally performing array change in the Z-axis direction to form a three-dimensional negative poisson ratio structure inner core, as shown in Step5 in fig. 2.
Step 3), importing a CAD model of the inner core of the three-dimensional negative poisson ratio structure into HYPERMESH software, performing geometric cleaning and grid division on the CAD model, and setting the material and the thickness of the inner core of the three-dimensional negative poisson ratio structure, wherein the material of the inner core of the three-dimensional negative poisson ratio structure is aluminum alloy, and the density of the inner core of the three-dimensional negative poisson ratio structure is 2810kg/m 3 The modulus of elasticity was 71GPa and the Poisson's ratio was 0.33.
And 4) introducing a traditional energy absorption box shell model without a three-dimensional negative poisson ratio structure inner core and a rigid wall model for testing collision into HYPERMESH, filling the three-dimensional negative poisson ratio structure inner core into the traditional energy absorption box shell to form a negative poisson ratio structure energy absorption box, setting the collision speed between the rigid wall and the negative poisson ratio structure energy absorption box to be 15km/h, restricting 6 degrees of freedom of a node which is not contacted with the rigid wall when the negative poisson ratio structure energy absorption box collides, and simultaneously defining contact and output between the rigid wall and the negative poisson ratio structure energy absorption box.
And 5) calculating the peak collision force P, the average collision force F, the compression displacement S and the mass m of the energy-absorbing box of the negative poisson ratio structure during collision according to the simulation output result.
Step 6), selecting an order of a high-order response surface model, taking a bottom edge length a, an included angle d between a bevel edge and the bottom edge, a vertical distance h between the two bottom edges, a thickness t of the negative poisson ratio unit cell structure and a width b of the negative poisson ratio unit cell structure corresponding to 80 groups of negative poisson ratio unit cell structures as inputs, and taking a peak collision force P, an average collision force F, a compression displacement S and a mass m of an energy absorption box corresponding to 80 groups of negative poisson ratio unit cell structures as outputs to construct the following four response surface models: the mass m response surface model, the compression displacement S response surface model, the average collision force F response surface model and the peak collision force P response surface model of the negative poisson ratio structure energy absorber box.
The order of the high-order response surface model is two-order, and the general form is as follows:
wherein m is the number of design parameters, x i And x j For input, y is the original response, a i 、a ii And a ij All are undetermined coefficients, the number of which is k and:
the mass response surface model, the compression displacement response surface model, the average collision force response surface model and the peak collision force response surface model of the negative poisson ratio structure energy absorption box are respectively as follows:
1) The response surface model of the negative poisson ratio structure energy absorption box mass m is as follows:
m＝3.408-0.2187a+0.3961b+0.0855h-0.0426d+0.957t+0.0052a 2 -0.0146b 2 -0.0000576h 2 +0.000176d 2 -0.022t 2 -0.0139ab-0.00272ah+0.00198ad-0.0313at-0.00094bh-0.00123bd+0.0864bt-0.000666hd-0.0055ht-0.00462dt
2) The response surface model of the negative poisson ratio structure energy absorption box compression displacement S is as follows:
S＝18.3507+6.4761a-3.9816b+2.2986h+1.2399d-28.604t-0.1569a 2 -2.3859b 2 -0.0877h 2 -0.00696d 2 +0.644t 2 +0.7614ab-0.1554ah-0.02834ad+1.546at+0.2692bh+0.07567bd-8.2472bt+0.0125hd+1.0947ht-0.1047dt
3) The response surface model of the average collision force F of the energy absorption box with the negative poisson ratio structure is as follows:
F＝135.9968-4.3789a+0.5376b-1.417h-1.0003d+21.253t+0.1228a 2 +2.3099b 2 +0.0478h 2 +0.0062d 2 +3.397t 2 -0.6732ab+0.1196ah+0.0206ad-1.2859at-0.2522bh-0.05623bd+7.818bt-0.0037hd-1.0269ht-0.02654dt
4) The response surface model of the negative poisson ratio structure energy absorption box peak collision force P is as follows:
P＝129.4295-3.4271a-0.0704b-2.6319h-0.5749d+116.2096t+0.2734a 2 +3.369b 2 +0.1481h 2 +0.0042d 2 +14.5422t 2 -1.1753ab+0.1665ah-0.0061ad-6.025at-0.3413bh+0.1725bd-2.6305bt-0.0196hd-1.6835ht-0.0027dt。
step 7), calculating correlation coefficients R of the four response surface model fits respectively 2 And root mean square error RMSE.
Step 8), for each response surface model, the correlation coefficient R thereof is calculated 2 The Root Mean Square Error (RMSE) is respectively compared with a preset first threshold value and a preset second threshold value; if the correlation coefficient R of four response surface models 2 Step 9) is executed when the first threshold value is equal to or greater than a preset first threshold value and the Root Mean Square Error (RMSE) is equal to or less than a preset second threshold value; otherwise, re-executing the steps 1) to 7) until the correlation coefficients R of the four response surface models 2 The root mean square error RMSE is equal to or greater than a preset first threshold value 0.92, and the root mean square error RMSE is equal to or less than a preset second threshold value 0.08.
And 9) taking the mass m and the compression displacement S of the energy-absorbing box with the negative poisson ratio structure as optimization targets, taking the peak collision force P, the average collision force F, the compression displacement S and the mass m as system constraint conditions, and taking the base length a of the negative poisson ratio unit structure, the included angle d of each inclined edge and the adjacent base, the vertical distance h between the two base, the thickness t of the negative poisson ratio unit structure and the width b of the negative poisson ratio unit structure as design variables to establish a mathematical model for optimizing the energy-absorbing box with the negative poisson ratio structure.
The mathematical model for negative poisson ratio structure energy-absorbing box optimization is as follows:
step 10), optimizing the bottom edge length a of the negative poisson ratio unit cell structure, the included angle d between each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative poisson ratio unit cell structure and the width b of the negative poisson ratio unit cell structure in Isight software by adopting a multi-target particle swarm optimization algorithm to obtain a Pareto solution set, and selecting a group of optimal solutions from the Pareto solution set.
The specific steps of the multi-objective particle swarm optimization algorithm are shown in fig. 5:
step1, initializing all particles with population size n, namely randomly setting the initial position and initial speed of each particle in a definition domain;
step2, calculating fitness function values of the particles, and forming a non-dominant solution set according to the dominant relationship;
step3, updating the external archive set;
step4, arranging crowded distances among particles of the external archive set in a descending order, checking whether the crowded distances exceed a preset rule number, and deleting non-dominant solutions outside the scale if the crowded distances exceed the preset rule number;
step5, updating the individual optimal position P best If the first generation is the first generation, the initial position of each particle is directly set as the optimal position P best If the updating is not the first generation, selecting whether to replace the updating according to the Pareto dominant relationship;
step6, randomly selecting a global optimal position G from the non-dominant solutions of the top 10% of the external archive set row best ；
Step7, updating a speed formula: v t+1 ＝w·v t +r 1 ·rand()·(p t -x t )+r 2 ·rand()·(G t -x t )
Wherein: omega is the inertial weight; r is (r) 1 、r 2 Is an acceleration constant; rand () is interval 0,1]Random numbers uniformly distributed on the base; p is p t 、G t The best position P of the particle itself at time t best And a global best position G best ；
Step8, updating the new generation position of each particle: x is x t+1 ＝x t +v t Wherein x is t 、v t The position and speed at time t;
step9, checking whether the maximum iteration number is reached, if so, terminating the program, and if not, continuing to start the loop from the second Step.
And 11) establishing a negative poisson ratio structure energy-absorbing box simulation model according to the optimized optimal solution, and carrying out solving calculation in LS-DYNA software to obtain an actual simulation result of the optimized negative poisson ratio structure energy-absorbing box. As shown in FIG. 6, the crash results of the energy-absorbing boxes are shown in FIG. 6, the compression displacement of the traditional energy-absorbing boxes is the largest among the three energy-absorbing boxes, the compression displacement of the energy-absorbing boxes with the negative poisson ratio structure before optimization is the second, the compression displacement of the energy-absorbing boxes with the negative poisson ratio structure after optimization is the smallest, the smaller the compression displacement of the energy-absorbing boxes is the larger the uncompressed space is, the larger the energy-absorbing potential of the energy-absorbing boxes is, and the energy-absorbing performance of the energy-absorbing boxes with the negative poisson ratio structure after optimization is effectively improved.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (8)
1. An energy-absorbing box that inside is provided with three-dimensional negative poisson's ratio structure inner core, its characterized in that: the energy-absorbing box comprises an energy-absorbing box body (1), a front mounting plate (2) and a rear mounting plate (5), wherein one end of the energy-absorbing box body (1) is connected with the front mounting plate (2), and the other end of the energy-absorbing box body (1) is connected with the rear mounting plate (5); the front mounting plate (2) is used for being connected with a beam of an automobile bumper through bolts, and the rear mounting plate (5) is used for being connected with a longitudinal beam of an automobile body through bolts;
the three-dimensional negative poisson ratio structure inner core comprises more than one basic unit, the basic unit comprises two negative poisson ratio unit structures, the bottom edges of the two negative poisson ratio unit structures are mutually orthogonal, the basic units are arrayed along the extending directions of the two ends of the vertical distance h between the two bottom edges, and the basic units are arrayed along the extending directions of the two ends of the length a of the two bottom edges;
the negative poisson ratio unit cell structure comprises two symmetrically parallel bottom edges, wherein the same sides of the two bottom edges are connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, and t is more than or equal to 0.6mm and less than or equal to 1.2mm; the widths of the first bevel edge, the second bevel edge and the bottom edge are b, and b is more than or equal to 2.2mm and less than or equal to 3mm; the included angle between each bevel edge and the adjacent bottom edge is d, and d is more than or equal to 55 degrees and less than or equal to 75 degrees; the length of the two bottom edges is a, and a is more than or equal to 12mm and less than or equal to 16mm; the vertical distance between the two bottom edges is h, and h is more than or equal to 8mm and less than or equal to 13mm;
the three-dimensional negative poisson ratio structure inner core is a square energy absorption carrier consisting of 22 x 9 x 4 = 792 negative poisson ratio unit cell structures.
2. The energy box with the inner core of the three-dimensional negative poisson's ratio structure arranged inside according to claim 1, wherein: the energy-absorbing box body (1) is of a hollow prismatic structure with an octagonal section, the whole surface of the energy-absorbing box body (1) comprises an upper surface, a lower surface, a left side surface, a right side surface and inclined side surfaces, the upper surface is symmetrically parallel to the lower surface, the left side surface is symmetrically parallel to the right side surface, the left side surface is perpendicular to the upper surface, the number of the inclined side surfaces is four, and the inclined side surfaces are respectively positioned between the upper surface and the right side surface, between the right side surface and the lower surface, between the lower surface and the left side surface and between the left side surface and the upper surface;
three first induction grooves (41) are symmetrically arranged on the left side surface and the right side surface, and the first induction grooves (41) are positioned at the quarter points of the axial length of the energy absorption box body (1); the upper surface is provided with two induction grooves II (42), the lower surface is provided with two induction grooves III, the induction grooves II (42) and the induction grooves III are mutually symmetrical, the induction grooves II (42) are positioned in the middle of the projection positions of the upper surfaces of the adjacent two induction grooves I (41), and the induction grooves III are positioned in the middle of the projection positions of the lower surfaces of the adjacent two induction grooves I (41); the second induction groove (42) and the first induction groove (41) are concave, the third induction groove is convex, and the depths of the first induction groove (41), the second induction groove (42) and the third induction groove are the same.
3. The energy absorber of claim 1, wherein the energy absorber comprises a three-dimensional negative poisson's ratio inner core: the thickness t of the first bevel edge, the second bevel edge and the bottom edge is 1.18mm; the width b of the first bevel edge, the second bevel edge and the bottom edge is 2.98mm; the included angle d between each bevel edge and the adjacent bottom edge is 56.1 degrees; the length a of the two bottom edges is 14.71mm; the vertical distance h between the two bottom edges is 8mm.
4. The multi-objective optimization method of the energy-absorbing box comprises the steps that a three-dimensional negative poisson ratio structure inner core is arranged in the energy-absorbing box, the three-dimensional negative poisson ratio structure inner core comprises more than one basic unit, the basic unit comprises two negative poisson ratio unit structures, each negative poisson ratio unit structure comprises two bottom edges which are symmetrically parallel, the same sides of the two bottom edges are connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, the widths of the first inclined edge, the second inclined edge and the bottom edge are b, the included angle d between each inclined edge and the adjacent bottom edge is a, the lengths of the two bottom edges are a, and the vertical distance between the two bottom edges is h; the three-dimensional negative poisson ratio structure inner core comprises more than one foundation unit, the foundation unit comprises two negative poisson ratio unit structures, the bottom edges of the two negative poisson ratio unit structures are mutually orthogonal, the foundation units are arrayed along the extending directions of the two ends of the vertical distance h between the two bottom edges, the foundation units are arrayed along the extending directions of the two ends of the length a of the two bottom edges,
the method is characterized in that: the method comprises the following steps:
step 1), in ISIGHT optimization software, an optimal Latin hypercube design method is selected, N groups of design sample points are uniformly selected within a threshold range preset by each design variable parameter, the design variable parameters are respectively the length a of the bottom edge of a negative Poisson ratio unit cell structure, the included angle d of each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative Poisson ratio unit cell structure and the width b of the negative Poisson ratio unit cell structure, N is a natural number larger than 0, and the N value is 80; the preset thresholds of the design variable parameters are respectively as follows: a=14mm, b=2.6mm, h=10.5mm, d=65°, t=0.9 mm; the change ranges of the preset threshold values are respectively as follows: a epsilon [12,16], b epsilon [2.2,3], h epsilon [8,13], d epsilon [55 DEG, 75 DEG ], t epsilon [0.6,1.2];
step 2), establishing CAD models of N groups of inner cores of the three-dimensional negative poisson ratio structures in CATIA software according to the selected design sample points;
the CAD model forming method of the three-dimensional negative poisson ratio structure inner core comprises the following detailed steps: according to the generated design sample points, a negative poisson ratio unit cell structure model is built in CATIA software; then, carrying out array change in the X-axis direction on the negative Poisson ratio unit cell structure model; then, replication change rotated by 90 degrees around the X axis is carried out; finally, performing array replication changes in the Y-axis direction and the Z-axis direction to form the inner core of the three-dimensional negative poisson ratio structure;
step 3), importing a CAD model of the inner core of the three-dimensional negative poisson ratio structure into HYPERMESH software, performing geometric cleaning and grid division on the CAD model, and setting the material and thickness of the inner core of the three-dimensional negative poisson ratio structure;
step 4), a traditional energy-absorbing box shell model without a three-dimensional negative poisson ratio structure inner core and a rigid wall model for testing collision are led into HYPERMESH, the three-dimensional negative poisson ratio structure inner core is filled in the traditional energy-absorbing box shell, the collision speed between the rigid wall and the energy-absorbing box with the three-dimensional negative poisson ratio structure inner core arranged inside is set, 6 degrees of freedom of a node which is not contacted with the rigid wall when the energy-absorbing box with the three-dimensional negative poisson ratio structure inner core is collided are restrained, and meanwhile contact and output between the rigid wall and the energy-absorbing box with the negative poisson ratio structure are defined;
step 5), calculating peak collision force P, average collision force F, compression displacement S and mass m of the energy-absorbing box with the inner core of the three-dimensional negative poisson ratio structure arranged inside during collision according to the simulation output result;
step 6), selecting an order of a high-order response surface model, taking a bottom edge length a, an included angle d between a bevel edge and the bottom edge, a vertical distance h between the two bottom edges, a thickness t of the negative poisson ratio unit cell structure and a width b of the negative poisson ratio unit cell structure corresponding to N groups of negative poisson ratio unit cell structures as inputs, and taking a peak collision force P, an average collision force F, a compression displacement S and a mass m of an energy absorption box corresponding to an energy absorption box with a three-dimensional negative poisson ratio structure inner core arranged in the N groups as outputs to construct the following four response surface models: the energy-absorbing box is internally provided with a mass m response surface model, a compression displacement S response surface model, an average collision force F response surface model and a peak collision force P response surface model of the energy-absorbing box with the inner core of the three-dimensional negative poisson ratio structure;
step 7), calculating correlation coefficients R of the four response surface model fits respectively 2 And a root mean square error RMSE;
step 8), for each response surface model, the correlation coefficient R thereof is calculated 2 The Root Mean Square Error (RMSE) is respectively compared with a preset first threshold value and a preset second threshold value; if the correlation coefficient R of four response surface models 2 Step 9) is executed when the first threshold value is equal to or greater than a preset first threshold value and the Root Mean Square Error (RMSE) is equal to or less than a preset second threshold value; otherwise, re-executing the steps 1) to 7) until the correlation coefficients R of the four response surface models 2 The Root Mean Square Error (RMSE) is equal to or greater than a preset first threshold value 0.92 and equal to or less than a preset second threshold value 0.08;
step 9), taking the mass m and the compression displacement S of the energy-absorbing box with the inner core of the three-dimensional negative poisson ratio structure as optimization targets, taking the peak collision force P, the average collision force F, the compression displacement S and the mass m as system constraint conditions, and taking the bottom edge length a of the negative poisson ratio unit structure, the included angle d of each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative poisson ratio unit structure and the width b of the negative poisson ratio unit structure as design variables to establish a mathematical model for optimizing the energy-absorbing box with the inner core of the three-dimensional negative poisson ratio structure;
step 10), optimizing the bottom edge length a of the negative poisson ratio unit cell structure, the included angle d between each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative poisson ratio unit cell structure and the width b of the negative poisson ratio unit cell structure in Isight software by adopting a multi-target particle swarm optimization algorithm according to the established optimized mathematical model to obtain a Pareto solution set, and selecting a group of optimal solutions from the Pareto solution set;
and 11) establishing an energy-absorbing box simulation model internally provided with the inner core of the three-dimensional negative poisson ratio structure according to the optimized optimal solution, and carrying out solving calculation in LS-DYNA software to obtain an actual simulation result of the energy-absorbing box internally provided with the inner core of the three-dimensional negative poisson ratio structure after optimization.
5. The method for multi-objective optimization of a crash box according to claim 4 wherein: the mass of the rigid wall in the step 4) is 900kg, and the collision speed between the rigid wall and the energy absorption box with the inner core of the three-dimensional negative poisson ratio structure arranged inside is 15km/h.
6. The method for multi-objective optimization of a crash box according to claim 4 wherein: the order of the high-order response surface model described in step 6) is second order, which is generally in the form of:
wherein m is the number of design parameters, x i And x j For input, y is the original response, a i 、a ii And a ij All are undetermined coefficients, the number of which is k and:
7. the method for multi-objective optimization of a crash box according to claim 4 wherein: in the step 6), a mass response surface model, a compression displacement response surface model, an average collision force response surface model and a peak collision force response surface model of the energy absorption box with the inner core of the three-dimensional negative poisson ratio structure are respectively as follows:
1) The response surface model of the energy-absorbing box mass m with the inner core of the three-dimensional negative poisson ratio structure is as follows:
m＝3.408-0.2187a+0.3961b+0.0855h-0.0426d+0.957t+0.0052a 2 -0.0146b 2 -0.0000576h 2 +0.000176d 2 -0.022t 2 -0.0139ab-0.00272ah+0.00198ad-0.0313at-0.00094bh-0.00123bd+0.0864bt-0.000666hd-0.0055ht-0.00462dt
2) The response surface model of the energy-absorbing box compression displacement S with the inner core of the three-dimensional negative poisson ratio structure is as follows:
S＝18.3507+6.4761a-3.9816b+2.2986h+1.2399d-28.604t-0.1569a 2 -2.3859b 2 -0.0877h 2 -0.00696d 2 +0.644t 2 +0.7614ab-0.1554ah-0.02834ad+1.546at+0.2692bh+0.07567bd-8.2472bt+0.0125hd+1.0947ht-0.1047dt
3) The response surface model of the energy-absorbing box average collision force F with the inner core of the three-dimensional negative poisson ratio structure is as follows:
F＝135.9968-4.3789a+0.5376b-1.417h-1.0003d+21.253t+0.1228a 2 +2.3099b 2 +0.0478h 2 +0.0062d 2 +3.397t 2 -0.6732ab+0.1196ah+0.0206ad-1.2859at-0.2522bh-0.05623bd+7.818bt-0.0037hd-1.0269ht-0.02654dt
4) The response surface model of the energy-absorbing box peak collision force P with the inner core of the three-dimensional negative poisson ratio structure is as follows:
P＝129.4295-3.4271a-0.0704b-2.6319h-0.5749d+116.2096t+0.2734a 2 +3.369b 2 +0.1481h 2 +0.0042d 2 +14.5422t 2 -1.1753ab+0.1665ah-0.0061ad-6.025at-0.3413bh+0.1725bd-2.6305bt-0.0196hd-1.6835ht-0.0027dt。
8. the method for multi-objective optimization of a crash box according to claim 4 wherein: the mathematical model for optimizing the energy absorption box, wherein the inner core of the three-dimensional negative poisson ratio structure is arranged in the step 9), is as follows:
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| CN106202758A (en) * | 2016-07-15 | 2016-12-07 | 南京航空航天大学 | A kind of bionical negative poisson's ratio construction car guard system and method for designing |
| CN208149239U (en) * | 2017-03-29 | 2018-11-27 | 南京航空航天大学 | Negative poisson's ratio single cell structure and three-dimensional negative poisson's ratio structure inner core and energy-absorption box |
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