CN111859671A - Shape-preserving topology optimization method considering suspension characteristic constraint - Google Patents
Shape-preserving topology optimization method considering suspension characteristic constraint Download PDFInfo
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Abstract
The invention discloses a shape-preserving topology optimization method considering overhang characteristic constraint, which divides a model into voxelized grids, and constructs shape-preserving units capable of keeping the appearance of the outer surface of a structure unchanged by taking a voxelized unit set as a reference; secondly, calculating the overhang angle and the horizontal distance of the shape-preserving unit facing to the process constraint requirement of additive manufacturing overhang characteristics, defining the overhang function of the shape-preserving unit, and sequencing the shape-preserving units from small to large according to the overhang function values; applying overhang feature constraints simulating addition and subtraction operations to the conformal units to ensure that new overhang structures are not generated during topology optimization; and in the iteration process, increasing and decreasing operations are performed on the shape-preserving units according to the sequencing order. The method can reduce the overhang structure of the inner layer of the structure which does not meet the self-supporting requirement of additive manufacturing under the condition of keeping the appearance of the outer layer of the structure unchanged, and improve the printability of the topology optimization design structure.
Description
Technical Field
The invention belongs to the technical field of structural optimization design for additive manufacturing, and particularly relates to a shape-preserving topology optimization method considering suspension characteristic constraints.
Background
Additive Manufacturing (AM) technology has been gaining attention in recent years and has been rapidly developed. Different from the traditional cutting machining manufacturing, the rapid manufacturing of the part is completed in an additive manufacturing mode of adding materials layer by layer and forming in an accumulation mode, and the influence of the geometric complexity of the part on the model manufacturing is eliminated to a great extent. Nevertheless, the additive manufacturing process itself still has certain process constraints on the optimal design of the parts. When the three-dimensional part model has an overhanging region, it is difficult to provide sufficient supporting force and heat transfer path because the lower layer is an overhanging region, so that the structure is easy to collapse or warp. While the addition of support structures can solve such problems to some extent, excessive support structure means additional material loss, increased forming time and post-processing work, and can also affect the internal stress distribution of the part. Therefore, in the process of structural optimization design, how to reduce the overhanging area of the optimized structure and reduce the usage amount of the supporting structure must be considered. In addition, in some engineering applications, in order to cope with different working conditions, the external appearance and the external size of the structure need to be ensured to be unchanged so as to fit the required working scene. How to optimize the suspension structure on the premise of keeping the external appearance of the structure is extremely important.
Disclosure of Invention
The invention provides a shape-preserving topology optimization method considering overhang feature constraint, and aims to reduce an overhang structure with a structure inner layer not meeting the self-supporting requirement of additive manufacturing and improve the printability of a topology optimization design structure.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method of guaranteed-appearance topology optimization taking into account drape-feature constraints, comprising the steps of:
s1, carrying out voxelization grid division on the structure model, wherein each voxel unit has a corresponding space coordinate;
s2, constructing shape preserving units capable of constraining the outer surface of the structure model by taking the voxel unit set as a reference, wherein each shape preserving unit comprises an outer surface unit, an inner unit and an inner surface unit of the structure model;
s3, two variation ways of controlling the conformal units are defined: a conformal unit increase operation, a conformal unit decrease operation;
s4, defining shape preserving unit suspension function, calculating suspension function value P of each shape preserving unit, and ordering shape preserving units from small to large according to suspension function value;
s5, setting a minimum self-supporting angle beta; finding the shape-preserving unit virtual increasing angle betaaoVirtual reduction angle beta of conformal unitdo(ii) a Setting an overhang angle constraint so that a new overhang angle beta is not generated in an iterative process oStructures smaller than the minimum support angle β;
s6, setting an iteration change rate l, determining an iteration change number S, applying the shape-preserving unit change method of the step S3 to the sequencing queue obtained in the step S4 according to the iteration change number, and performing increasing or decreasing operation on the shape-preserving units; applying the overhang angle constraint set in step S5 at the current step, without performing an increase operation and a decrease operation on the constrained conformal units;
s7, resetting the virtual increasing and virtual decreasing angle constraints of all conformal units, and judging again in the next iteration;
s8, iteratively circulating the steps S4 to S7 until the structure inner surface is totally overhung by the structure angle betaoAnd when the value is more than or equal to beta, the iteration is terminated.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, the shape-cell increasing operation in step S3 is: on one side of the inner surface of the shape-preserving unit, a voxel unit is added from the outer surface of the structure model to the inner surface; conformal cell reduction operates as: on the inner surface side of the conformal unit, one voxel unit is deleted from the inner surface to the outer surface direction of the structural model.
Further, the conformal cell dangling function defined in step S4 is shown as equation (1), where equation (1) is as follows:
Wherein q is the self-defined coefficient of the ordering coefficient, betaoFor the overhang structure angle, h is the overhang structure horizontal distance, and p is the overhang function value for the conformal unit.
Further, in the x, z plane, the overhang structure angle βoThe calculation method is as follows:
1) making a suspension filter ring with the radius of q at the position of coordinates (x, z) of the unit body on the inner surface of the conformal unit;
2) traversing voxel units in the filter ring, and finding an inner surface unit body with the maximum distance from the center unit body of the circle as the coordinate (x, Z) and the negative direction of the Z axis as the coordinate (r, t);
3) calculating the overhang angle beta according to the formula (2)oIn the formula (2), x, z, r, and t are voxel unit coordinates.
Further, in the x and z planes, the horizontal direction distance h is obtained as follows:
1) calculating the suspension angle beta of the suspension structure where all the conformal units are positionedoThen, beta is mixedoThe conformal units of beta or more are marked as self-supporting units;
2) traversing along the negative direction of the z axis by taking the coordinates (X, z) of the unit bodies on the inner surface of the conformal unit as a starting point until the z is equal to 0, and traversing along the suspension direction of the X axis when a new row is traversed; when traversing to the first self-supporting unit body, taking the self-supporting unit body, recording the coordinates as (a, c), and ending the traversal; if the self-supporting unit body is not traversed, the unit body which is farthest from the central unit body in the x direction is taken, and the coordinates are marked as (a, c);
3) The horizontal direction distance h is obtained by the following equation (3), where dx is the edge length of each voxel unit, and x and a are the voxel unit coordinates.
h＝|x-a|×dx (3)
Further, in step S5, the overhang angle constraint set is: when beta isaoWhen the support angle is smaller than the minimum support angle beta, no additional operation is performed on the shape-preserving unit in the current iteration step; when beta isdoLess than the minimum support angle β, no reduction is performed on the conformal unit in the current iteration step.
Further, the dummy increase angle β of the shape cell in the x, z planeaoVirtual reduction angle beta of conformal unitdoThe calculation method comprises the following steps:
1) according to the calculation of the angle beta of the suspension structureoCalculating the dummy increase angle beta of the conformal unitao；
2) a, simulating an inner surface unit after reduction operation is executed on a current conformal unit, namely taking a unit body with coordinates (x, z) as a circle center and making a suspension filter ring with the radius q;
b. traversing voxel units in the filter ring, and finding an inner surface unit body with the largest distance from the circle center unit body in the positive direction of the Z axis, wherein the coordinate is (r, t);
c. calculating the overhang angle beta according to the formula (2)doAnd x, z, r and t are voxel unit coordinates.
Further, in step S6, specifically, the conformal unit with the smaller value of the overhang function obtained in step S5 is regarded as being in the large overhang structure, and is removed; regarding the shape preserving unit with larger suspension function value as being in a small suspension structure for filling; executing conformal unit reduction operation on conformal units from 0 th to S, except for p being 1, in the queue sorted from small to large; a conformal unit add operation is performed on the (A-S) th to A-th conformal units in the queue, A being the total number of conformal units.
Further, the iteration change number S ═ l × a.
The invention has the beneficial effects that: 1. the invention defines the shape-preserving unit, and can ensure that the appearance of the outer surface of the structure is not changed in the optimization process;
2. the suspension function defined by the invention can quantitatively express the size of the suspension structure, and the parameter solving method is suitable for a structure model based on voxel unit division.
3. The invention sets the overhang function and the overhang constraint of simulation increase and reduction operation, and the combination of the two ideas can ensure that a new overhang structure is not generated in the process of generating the self-supporting structure and reducing the overhang structure, thereby better optimizing the inner surface of the structure.
Drawings
FIG. 1 is a schematic diagram of the structural model voxelization meshing of the present invention.
FIG. 2 is a schematic view of a six-way conformal cell of the present invention.
FIG. 3 is a schematic view of the same conformal unit add and subtract operation of the present invention, wherein (a) is the initial conformal unit; (b) is a conformal unit after performing the reduction operation; (c) is the conformal unit after the add operation is performed.
FIG. 4 is a schematic of the dangling function ordering of the present invention.
FIG. 5 is a schematic diagram of a method for obtaining a correlation coefficient in a suspension function under a certain suspension structure according to the present invention.
FIG. 6 is a schematic diagram of a method for determining the virtual overhang increasing angle according to the present invention.
Fig. 7 is a schematic diagram of the method for determining the suspension virtual reduction angle according to the present invention.
FIG. 8a is a semi-transparent view of the initial structural model of the present invention.
FIG. 8b is a semi-transparent view of the optimized structural model of the present invention.
FIG. 8c is a cross-sectional view of the initial model of the present invention.
Figure 8d is a cross-sectional view of the optimized structure of the present invention.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
The invention provides a shape-preserving topology optimization method considering overhang characteristic constraint, which comprises the following steps of:
s1, as shown in fig. 1, performing voxelization mesh division on the structure model, where each voxel unit has its corresponding spatial coordinate (x, y, z);
s2, as shown in fig. 2, constructing conformal units (hereinafter referred to as conformal units) capable of constraining six directions of the outer surface of the structural model based on the voxel unit set, each of the conformal units including an outer surface unit, an inner unit and an inner surface unit of the structural model; the six directions are positive and negative directions along x, y and z axes, respectively, wherein the directions 1 and 2 conformal units are parallel to the z axis, the directions 3 and 4 conformal units are parallel to the y axis, the directions 5 and 6 conformal units are parallel to the x axis, and the conformal units are represented by B. The black cells in fig. 2 are the cells on the outer surface of the structural model, and no change is made to the cells; the white unit is an internal unit of the structural model; the gray cells are the surface cells in the structural model, and the total number of conformal cells is A.
S3, as shown in FIG. 3, the black cells are structural outer surface cells; the white unit is a structural internal unit; the grey units are structural inner surface units; two variations of controlling conformal units are defined: a conformal unit increase operation, a conformal unit decrease operation;
(1) conformal unit reduction operation: on the inner surface side of the conformal cells, one voxel cell is deleted from the inner surface to the outer surface direction of the model, as shown in fig. 3 (b).
(2) Conformal unit addition operation: on the inner surface side of the conformal unit, a voxel unit is added from the outer surface of the model to the inner surface, as shown in fig. 3 (c).
S4, defining a conformal cell suspension function (equation 1), calculating a suspension function value P for each conformal cell, and ordering the conformal cells by the suspension function value from small to large.
Wherein q is the self-defined coefficient of the ordering coefficient, betaoAnd calculating a suspension function value p of each conformal unit for the suspension structure angle and h for the suspension structure horizontal distance, assigning p to the corresponding conformal unit, and sequencing the conformal units according to the suspension function value p. The sorting function is as follows:
FIG. 4 is a graph of the drape function, where the drape function is plotted for only a portion of the angles, the same drape angle β oThe larger the horizontal distance h is, the smaller the suspension function value p is; same horizontal distance h and overhang angle betaoThe smaller the value of the pendancy function p; q influences the slope of the droop function, initiallyThe larger the q set the faster the drape function value drops.
For example, in fig. 5, an overhang structure is illustrated in x and z planes, where black unit cells are structural outer surface unit cells, and gray voxel unit sets are conformal units to be optimized:
(1) angle beta of overhang structureoThe calculation method is as follows:
a. a pendulous filter circle of radius q is made at the conformal unit inner surface unit volume (coordinates (x, z)).
b. And traversing voxel units in the filter circle to find an inner surface unit body (oblique line filling unit body) (the coordinate is (r, t)) which has the largest distance from a center unit body (the coordinate is (x, Z)) in the Z axis negative direction.
c. Calculating the overhang angle beta according to the formula (2)oAnd x, z, r and t are voxel unit coordinates.
(2) The horizontal vertical distance h is obtained as follows:
a. calculating the suspension angle beta of the suspension structure where all the conformal units are positionedoThen, beta is mixedoConformal units of ≧ β are labeled self-supporting units.
b. Traversing along the Z-axis negative direction until Z is 0 by taking the conformal unit inner surface unit body (coordinates are (X, Z)) as a starting point, traversing along the X-axis suspension direction when traversing to a new row, and taking the self-supporting unit body (coordinates of a vertical line filling unit body are (a, c) in the graph of fig. 5) to finish traversing when traversing to the first self-supporting unit body; if the self-supporting unit body is not traversed, the unit farthest from the central unit body (the coordinate is (x, z)) in the x direction is taken, and the coordinate is marked as (a, b).
c. And (3) calculating the horizontal vertical distance h, wherein dx is the edge length of each voxel unit, and x and a are the coordinates of the voxel unit.
h＝|x-a|×dx (3)
S5, setting the minimum self-supporting angle β, i.e. considering the suspension angle greater than or equal to β is not optimized.
In the practical optimization process, the thickness of some large overhanging structure parts is very thin, the strength is low, and the situations of fracture, deformation and the like are easy to generate in the use process, so the thickness increasing operation needs to be performed on the shape-preserving units of the part structures, the thickness of the part is increased, and the structural strength is increased. Considering the constraint of the overhang structure, if the lower part is suspended to be greatly increased, larger overhang structure can be generated, and virtual increase overhang constraint is applied to the shape-preserving unit needing to be increased; in some structural optimization taking reduction of the structural weight as a main optimization target, the thickness of some large overhanging parts of the structure is very thick, the thickness reduction operation needs to be performed on the shape-preserving units of the part of the structure to reduce the thickness of the structure so as to further reduce the weight of the structure, the overhanging structure constraint is considered, if the structure is also an overhanging structure, the reduction operation may generate a larger overhanging structure, and the virtual reduction overhanging constraint is applied to the shape-preserving units needing the reduction operation, and the method is as follows:
Traversing all the shape-preserving units, performing increase and decrease operations on the shape-preserving unit simulation, and obtaining the virtual increase angle beta of the shape-preserving unitaoVirtual reduction angle beta of conformal unitdo；
Setting an overhang angle constraint, wherein the overhang constraint is as follows: when beta isaoWhen the support angle is smaller than the minimum support angle beta, no additional operation is allowed to be performed on the shape-preserving unit in the current iteration step; when beta isdoLess than the minimum support angle β, the reduction operation is not allowed to be performed on this conformal unit in the current iteration step to ensure that no new overhang angle β is generated during the iteration processoA structure smaller than beta.
Conformal unit overhang virtual increase angle betaaoConformal unit overhang virtual reduction angle betadoThe calculation method is as follows:
(1) as shown in FIG. 6, the gray portion is the quasi-optimized conformal unit, the black unit is the outer surface unit, the vertical line filling unit is the structural inner surface unit, the dashed frame diagonal line filling unit is the added unit for simulating the adding operation, and the overhanging structure angle β is obtained according to the (1) th portion in step 5 with the diagonal line filling unit as the centeroThe method for calculating the virtual increase angle beta of conformal unitao。
(2) As shown in fig. 7, the gray portion is the conformal unit to be optimized, the black unit is the outer surface unit, the vertical line filling unit body is the structural inner surface unit, the dotted line frame gray unit is the unit to be removed, and the oblique line filling unit is the inner surface unit after the reduction operation is performed for the current conformal unit simulation, and then:
a. A dangling filter circle of radius q is made at the diagonal fill cell (coordinates (x, z)).
b. And traversing voxel units in the filter circle to find an inner surface unit body (vertical line filling unit body) (the coordinate is (r, t)) which has the largest distance from the center unit body (the coordinate is (x, Z)) in the positive direction of the Z axis.
c. Calculating the overhang angle beta according to the formula (2)doAnd x, z, r and t are voxel unit coordinates.
S6, setting an iteration change rate l (l is more than or equal to 0 and less than or equal to 0.5), and determining the iteration change number S to obtain the number according to the formula (4), wherein A is the total number of the conformal units. Conforming units (beta) with smaller p values are processed according to the overhanging function of step 5oSmaller or larger) is considered to be in a large overhang configuration and needs to be removed; conformal units (beta) with larger p valuesoLarger or smaller) are considered to be in a relatively small overhang structure, only padding is needed. Applying the conformal cell change method of step S3 to the sorted queue obtained in step S4 according to the iteration change number, and performing an increase or decrease operation on the conformal cells. Performing conformal unit reduction operation on conformal units from 0 th to S (except for p being 1) in the queue sorted from small to large; a conformal unit add operation is performed on the (a-S) to a-th conformal unit in the queue.
S＝l×A (4)
The overhang angle constraint set in step S5 is applied in the current step, and no increase operation and decrease operation are performed on the constrained conformal units.
S7, resetting the virtual increasing and virtual decreasing angle constraints of all conformal units, and judging again in the next iteration;
s8, iteratively looping steps S4 through S7, recalculating the overhang function value and assigning a corresponding conformal unit according to step S4 for each iteration, applying the overhang angle constraint of step S5 during the iteration,changing the conformal units according to the rules of step S6; up to the angle beta of all the suspension structures in the housing structureoAnd when the value is more than or equal to beta, the iteration is terminated.
FIG. 8 shows the initial overhang angle βoIs 30 degrees, the minimum self-supporting angle beta is set to be 45 degrees, and the optimization result after the method is applied is compared with a graph. The optimization result shows that the method can improve the internal suspension structure of the structure according to the set minimum self-supporting angle under the condition of keeping the appearance of the outer surface of the structure unchanged.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.
Claims (10)
1. A method for shape preserving topology optimization taking into account drape feature constraints, comprising the steps of:
s1, carrying out voxelization grid division on the structure model, wherein each voxel unit has a corresponding space coordinate;
s2, constructing shape preserving units capable of constraining the outer surface of the structure model by taking the voxel unit set as a reference, wherein each shape preserving unit comprises an outer surface unit, an inner unit and an inner surface unit of the structure model;
s3, two variation ways of controlling the conformal units are defined: a conformal unit increase operation, a conformal unit decrease operation;
s4, defining shape preserving unit suspension function, calculating suspension function value P of each shape preserving unit, and ordering shape preserving units from small to large according to suspension function value;
s5, setting a minimum self-supporting angle beta; finding the shape-preserving unit virtual increasing angle betaaoVirtual reduction angle beta of conformal unitdo(ii) a Setting an overhang angle constraint so that a new overhang angle beta is not generated in an iterative processoStructures smaller than the minimum support angle β;
s6, setting an iteration change rate l, determining an iteration change number S, applying the shape-preserving unit change method of the step S3 to the sequencing queue obtained in the step S4 according to the iteration change number, and performing increasing or decreasing operation on the shape-preserving units; applying the overhang angle constraint set in step S5 at the current step, without performing an increase operation and a decrease operation on the constrained conformal units;
S7, resetting the virtual increasing and virtual decreasing angle constraints of all conformal units, and judging again in the next iteration;
s8, iteratively circulating the steps S4 to S7 until the structure inner surface is totally overhung by the structure angle betaoAnd when the value is more than or equal to beta, the iteration is terminated.
2. The shape-preserving topology optimization method of claim 1, wherein in step S2, the constructed conformal units are capable of constraining six directions of the outer surface of the structure model, the six directions being positive and negative along x, y, and z axes, respectively.
3. The shape-preserving topology optimization method of claim 1, wherein: the shape cell increasing operation in step S3 is: on one side of the inner surface of the shape-preserving unit, a voxel unit is added from the outer surface of the structure model to the inner surface; conformal cell reduction operates as: on the inner surface side of the conformal unit, one voxel unit is deleted from the inner surface to the outer surface direction of the structural model.
4. The shape preserving topology optimization method of claim 1, wherein the conformal cell suspension function defined in step S4 is represented by equation (1), wherein equation (1) is as follows:
p＝1(βo≥β)
wherein q is a custom coefficient, betaoFor the overhang structure angle, h is the overhang structure horizontal distance, and p is the overhang function value for the conformal unit.
5. The shape preserving topology optimization method of claim 4, wherein in the x, z plane, the overhang structure angle βoThe calculation method is as follows:
1) making a suspension filter ring with the radius of q at the position of coordinates (x, z) of the unit body on the inner surface of the conformal unit;
2) traversing voxel units in the filter ring, and finding an inner surface unit body with the maximum distance from the center unit body of the circle as the coordinate (x, Z) and the negative direction of the Z axis as the coordinate (r, t);
3) calculating the overhang angle beta according to the formula (2)oIn the formula (2), x, z, r, and t are voxel unit coordinates.
6. The shape-preserving topology optimization method of claim 4, wherein in the x, z plane, the distance h in the horizontal direction is obtained as follows:
1) calculating the suspension angle beta of the suspension structure where all the conformal units are positionedoThen, beta is mixedoThe conformal units of beta or more are marked as self-supporting units;
2) traversing along the Z-axis negative direction until Z is 0 by taking the coordinates (X, Z) of the shape-preserving unit inner surface unit body as a starting point, and traversing along the X-axis suspension direction when a new row is traversed; when traversing to the first self-supporting unit body, taking the self-supporting unit body, recording the coordinates as (a, c), and ending the traversal; if the self-supporting unit body is not traversed, the unit body which is farthest from the central unit body in the x direction is taken, and the coordinates are marked as (a, c);
3) The horizontal direction distance h is obtained by the following equation (3), where dx is the edge length of each voxel unit, and x and a are the voxel unit coordinates.
h＝|x-a|×dx
7. The shape-preserving topology optimization method of claim 1, wherein in step S5, the overhang angle constraint is set as: when beta isaoIs less thanWhen the supporting angle beta is the minimum, no additional operation is performed on the shape-preserving unit in the current iteration step; when beta isdoLess than the minimum support angle β, no reduction is performed on the conformal unit in the current iteration step.
8. The shape-preserving topology optimization method of claim 5, wherein in step S5, the dummy cell is increased by an angle β in the x, z planeaoVirtual reduction angle beta of conformal unitdoThe calculation method comprises the following steps:
1) according to the calculation of the angle beta of the suspension structureoCalculating the dummy increase angle beta of the conformal unitao；
2) a, simulating an inner surface unit after reduction operation is executed on a current conformal unit, namely taking a unit body with coordinates (x, z) as a circle center and making a suspension filter ring with the radius q;
b. traversing voxel units in the filter ring, and finding an inner surface unit body with the largest distance from the circle center unit body in the positive direction of the Z axis, wherein the coordinate is (r, t);
c. calculating the overhang angle beta according to the formula (2) doAnd x, z, r and t are voxel unit coordinates.
9. The shape-preserving topology optimization method of claim 1, wherein step S6 is to remove the conformal unit with smaller suspension function value obtained in step S5 as the conformal unit in the large suspension structure; regarding the shape preserving unit with larger suspension function value as being in a small suspension structure for filling; executing conformal unit reduction operation on conformal units from 0 th to S, except for p being 1, in the queue sorted from small to large; a conformal unit add operation is performed on the (A-S) th to A-th conformal units in the queue, A being the total number of conformal units.
10. The shape-preserving topology optimization method of claim 9, wherein the number of iterative changes S ═ lxa.
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