CN111859671A - A Shape Preserving Topology Optimization Method Considering Dangling Feature Constraints - Google Patents

Abstract

The invention discloses a shape-preserving topology optimization method considering overhang feature constraints. The model is divided into voxelized grids, and the voxel unit set is used as a benchmark to construct a shape-preserving unit that can keep the outer surface topography of the structure unchanged; Additive manufacturing overhang feature process constraint requirements, calculate the overhang angle and horizontal distance of the conformal unit, define the conformal unit overhang function, and sort the conformal units according to the value of the overhang function from small to large; apply a simulation increase to the conformal unit , Reduce the overhang feature constraint of the operation to ensure that no new overhang structure is generated during the topology optimization process; in the iterative process, the increase and decrease operations are performed on the conformal elements according to the sorting order. The method can reduce the overhanging structure of the inner layer of the structure that does not meet the self-supporting requirements of additive manufacturing under the condition of keeping the topography of the outer layer of the structure unchanged, and improve the printability of the topology optimized design structure.

Description

A Shape Preserving Topology Optimization Method Considering Dangling Feature Constraints

technical field

The invention belongs to the technical field of structural optimization design oriented to additive manufacturing, and particularly relates to a shape-preserving topology optimization method considering overhang feature constraints.

Background technique

Additive Manufacturing (AM) technology has attracted a lot of attention in recent years and has developed rapidly. Different from traditional cutting manufacturing, additive manufacturing uses layer-by-layer material addition and cumulative molding to complete the rapid manufacturing of parts, which largely eliminates the impact of the geometric complexity of the parts on model manufacturing. Nevertheless, the additive manufacturing process itself still has certain process constraints on the optimal design of parts. When there is an overhang area in the 3D part model, it is difficult to provide sufficient support force and heat transfer path because the lower layer is an overhang area, which makes the structure prone to collapse or warp. Although adding support structures can solve such problems to a certain extent, too much support structure means additional material loss, increased forming time and post-processing work, and may also affect the internal stress distribution of the part. Therefore, in the process of structural optimization design, it is necessary to consider how to reduce the overhang area of the optimized structure and reduce the usage of the supporting structure. In addition, in some engineering applications, in order to cope with different working conditions, it is necessary to ensure that the external appearance of the structure and its external dimensions remain unchanged, so as to fit the required working scene. How to optimize the overhang structure on the premise of maintaining the external appearance of the structure is particularly important.

SUMMARY OF THE INVENTION

The invention provides a shape-preserving topology optimization method considering overhang feature constraints, and aims to reduce overhang structures whose inner layers of the structure do not meet the self-supporting requirements of additive manufacturing, and improve the printability of the topology optimization design structure.

To achieve the above object, the present invention adopts the following technical solutions:

A shape-preserving topology optimization method considering dangling feature constraints, including the following steps:

S1. The structural model is divided into voxelized grids, and each voxel unit has its corresponding spatial coordinates;

S2. Based on the voxel unit set, construct a conformal unit capable of constraining the outer surface of the structural model, and each conformal unit includes an exterior surface unit, an interior unit and an interior surface unit of the structural model;

S3. Define two variations of controlling the conformal unit: the increase operation of the conformal unit and the decrease of the conformal unit;

S4, define the drape function of the conformal unit, calculate the drape function value P of each conformal unit, and sort the conformal units according to the drape function value from small to large;

S5. Set the minimum self-supporting angle β; obtain the virtual increase angle β _ao of the conformal element and the virtual decrease angle β _do of the conformal element; set the overhang angle constraint so that no new overhang angle β _o is generated during the iteration process Structures smaller than the minimum support angle β;

S6, set the iterative change rate 1, determine the iterative change number S, apply the shape-preserving unit changing method of step S3 to the sorting queue obtained in step S4 according to the iterative change number, and perform an increase or decrease operation on the shape-preserving unit; in the current step The suspension angle constraint set in step S5 is applied, and the increase operation and decrease operation are not performed on the constrained conformal unit;

S7, reset the virtual increase and virtual decrease angle constraints for all conformal units, and re-determine in the next iteration;

S8. Iteratively loops steps S4 to S7 until all the overhanging structure angles β _o ≥ β on the inner surface of the structure, the iteration is terminated.

In order to optimize the above technical solutions, the specific measures taken also include:

Further, in step S3, the increase operation of the conformal unit is: on the inner surface side of the conformal unit, add a voxel unit from the outer surface of the structural model to the inner surface direction; the decrease operation of the conformal unit is: on the conformal unit On the inner surface side of the structure model, one voxel unit is deleted from the inner surface of the structural model to the outer surface.

Further, the shape-preserving element drape function defined in step S4 is shown in formula (1), and formula (1) is as follows:

In the formula, q is the self-defined coefficient of sorting coefficient, β _o is the angle of the overhanging structure, h is the horizontal distance of the overhanging structure, and p is the overhang function value of the conformal element.

Further, in the x and z planes, the overhanging structure angle β _o is calculated as follows:

1) On the inner surface unit of the conformal unit, the coordinates are (x, z) to make a pendant filter circle with a radius of q;

2) Traverse the voxel units in the filter circle, and find the inner surface unit body whose coordinates are (x, z) from the center of the circle and the largest distance in the negative direction of the Z axis, and the coordinates are (r, t);

3) Obtain the overhang angle β _o according to the formula (2), the formula (2) is as follows, and x, z, r, and t are the coordinates of the voxel unit.

Further, in the x and z planes, the horizontal distance h is calculated as follows:

1) After obtaining the overhang angle β _o of the overhanging structure where all the conformal units are located, mark the conformal units with β _o ≥ β as self-supporting units;

2) Take the inner surface unit body of the conformal unit, and the coordinates are (x, z) as the starting point to traverse along the negative direction of the z-axis until z=0. Every time a new line is traversed, it is traversed in the hanging direction of the X-axis; When a self-supporting unit is taken from the supporting unit, the coordinates are marked (a, c), and the traversal is ended; if the self-supporting unit is not traversed, the unit that is farthest from the center unit in the x direction is taken, and the coordinates are marked as (a, c);

3) Calculate the distance h in the horizontal direction according to formula (3), formula (3) is as follows, 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)

Further, in step S5, the set overhang angle constraint is: when β _ao is less than the minimum support angle β, in the current iteration step, no increase operation is performed on this conformal unit; when β _do is less than the minimum support angle β, in the For the current iteration, no reduction operation is performed for this conformal element.

Further, in the x, z plane, the virtual increase angle β _ao of the conformal element and the virtual decrease angle β _do of the conformal element are calculated as follows:

1) Obtain the virtual increase angle β _ao of the conformal element according to the method for obtaining the overhang structure angle β _o ;

2) a. Simulate the inner surface unit after the reduction operation is performed in the current conformal unit, that is, the unit body at the coordinates (x, z) is the center of the circle, and a suspension filter circle with a radius of q is used;

b. Traverse the voxel units in the filter circle to find the inner surface unit body with the largest distance from the center unit body in the positive direction of the Z axis, and the coordinates are (r, t);

c. Obtain the overhang angle β _do according to formula (2), where x, z, r, and t are the coordinates of the voxel unit.

Further, step S6 is specifically as follows: the conformal unit with a smaller overhang function value obtained in step S5 is regarded as being in a large overhang structure and removed; the conformal unit with a larger overhang function value is regarded as being in a small overhang structure. , perform padding; perform the conformal unit reduction operation on the conformal units 0 to S except p=1 in the queue sorted from small to large; perform the conformal unit reduction operation on the (A-S) to A conformal units in the queue Add operation of shape unit, A is the total number of shape-keeping units.

Further, the number of iterative changes S=l×A.

The beneficial effects of the present invention are: 1. The present invention defines a conformal unit, which can ensure that the topography of the outer surface of the structure does not change during the optimization process;

2. The overhang function defined in the present invention can quantify the size of the overhang structure, and the parameter calculation method is suitable for the structure model based on the division of voxel units.

3. The present invention sets the drape function and the drape constraint for simulating the increase and decrease operations. The combination of the two ideas can ensure that no new drape structure is generated in the process of generating the self-supporting structure and reducing the drape structure. The inner surface of the structure is optimized.

Description of drawings

Fig. 1 is a schematic diagram of the voxelized mesh division of the structure model of the present invention.

Fig. 2 is a schematic diagram of the six-direction conformal unit of the present invention.

Fig. 3 is a schematic diagram of increasing and decreasing operations of the same conformal unit of the present invention, wherein (a) is the initial conformal unit; (b) is the conformal unit after performing the decreasing operation; (c) is the preserving unit after performing the increasing operation shape unit.

Fig. 4 is a schematic diagram of the ordering of the drape function 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 of the present invention.

FIG. 6 is a schematic diagram of the method for obtaining the virtual increase angle of the overhang according to the present invention.

FIG. 7 is a schematic diagram of the method for obtaining the drape virtual reduction angle of the present invention.

Figure 8a, 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.

Figure 8c, a cross-sectional view of the initial construction model of the present invention.

Fig. 8d is a cross-sectional view of the optimized structure of the present invention.

Detailed ways

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 feature constraints, comprising the following steps:

S1. As shown in Figure 1, the structural model is divided into voxelized grids, and each voxel unit has its corresponding spatial coordinates (x, y, z);

S2. As shown in Figure 2, using the voxel unit set as a benchmark, construct conformal units (hereinafter referred to as conformal units) that can constrain the outer surface of the structural model in six directions, each conformal unit includes the outer surface of the structural model. Surface unit, interior unit and interior surface unit; the six directions are the positive and negative directions along the x, y, and z axes, respectively, where the conformal units in directions 1 and 2 are parallel to the z-axis, and the conformal units in directions 3 and 4 are parallel to the z-axis. The y-axis, directions 5 and 6 conformal elements are parallel to the x-axis, and the conformal elements are denoted by B. In Figure 2, the black elements are the outer surface elements of the structural model, and no changes are made to them; the white elements are the internal elements of the structural model; the gray elements are the inner surface elements of the structural model, and the total number of conformal elements is A.

S3. As shown in Figure 3, the black unit is the outer surface unit of the structure; the white unit is the inner unit of the structure; the gray unit is the inner surface unit of the structure; define two variations of controlling the conformal unit: adding operations to conformal units, conformal units unit reduction operation;

(1) Conformal unit reduction operation: On the inner surface side of the conformal unit, delete one voxel unit from the inner surface of the model to the outer surface, as shown in Figure 3(b).

(2) Conformal unit addition operation: On the inner surface side of the conformal unit, add a voxel unit from the outer surface of the model to the inner surface, as shown in Figure 3(c).

S4. Define the drape function of the conformal unit (Equation 1), calculate the drape function value P of each conformal unit, and sort the conformal units according to the drape function value from small to large.

where q is the sorting coefficient and is a custom coefficient, β _o is the angle of the overhang structure, h is the horizontal distance of the overhang structure, calculate the overhang function value p of each conformal unit, and assign p to the corresponding conformal unit, according to the overhang function value p Sort conformal cells. The sorting function is as follows:

Fig. 4 is an image of the drape function, in which only the drape function at some angles is drawn. For the same drape angle β _o , the larger the horizontal distance h, the smaller the drape function value p; the same horizontal distance h, the smaller the drape angle β _o , The smaller the drape function value p;

As shown in Figure 5, an overhanging structure is taken as an example on the x and z planes, in which the black unit is the outer surface unit of the structure, and the gray voxel unit set is the conformal unit to be optimized:

(1) The calculation method of the overhanging structure angle β _o is as follows:

a. Make a pendant filter circle with radius q at the inner surface unit body of the conformal unit (coordinates are (x, z)).

b. Traverse the voxel units in the filter circle to find the inner surface unit body (the oblique line fills the unit body) with the largest distance from the center unit body (coordinates are (x, z)) in the negative direction of the Z axis (coordinates are (r, t)) .

c. Obtain the overhang angle β _o according to formula (2), and x, z, r, and t are the coordinates of the voxel unit.

(2) The horizontal and vertical distance h is calculated as follows:

a. After obtaining the overhang angle β _o of the overhanging structure where all conformal units are located, mark the conformal units with β _o ≥ β as self-supporting units.

b. Take the inner surface unit body of the conformal unit (coordinates are (x, z)) as the starting point and traverse along the negative direction of the Z-axis until Z=0. When traversing a new line, traverse in the hanging direction of the X-axis. When the first self-supporting unit body is taken from the self-supporting unit body (the coordinates of the vertical line filling unit body in Figure 5 are (a, c)), the traversal ends; if the self-supporting unit body is not traversed, the distance from the center unit body in the x direction is taken ( The farthest cell with coordinates (x, z)) has coordinates (a, b).

c. Calculate the horizontal and vertical distance h according to formula (3), 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. Set the minimum self-supporting angle β, that is, when the overhang angle is considered to be greater than or equal to β, it is a self-supporting structure and does not need to be optimized.

In the actual optimization process, the thickness of some large overhanging structures is very thin, and the strength is low, and it is easy to cause fracture and deformation during use. Therefore, it is necessary to increase the thickness of the conformal unit of this part of the structure to increase the thickness of this part. increase the structural strength. Considering the overhang structure constraints, if the lower overhang is larger, the increase operation may generate a larger overhang structure, and imaginary increase overhang constraints are imposed on the conformal elements that need to be increased. Some large overhanging parts of the structure are very thick, and the conformal unit of this part of the structure needs to perform a thickness reduction operation to reduce the thickness of the structure and further reduce the weight of the structure. Considering the constraints of the overhanging structure, if the upper part of the structure is also Overhang structure, reduce operation may produce larger overhang structure, impose virtual reduce overhang constraint on conformal elements that need reduction operation, as follows:

Traverse all the conformal units, perform the increase and decrease operations on the conformal unit simulation, and obtain the virtual increase angle β _ao of the conformal unit and the virtual decrease angle β _do of the conformal unit;

Set the overhang angle constraint, and set the overhang constraint as: when β _ao is less than the minimum support angle β, in the current iteration step, it is not allowed to perform addition operations on this conformal element; when β _do is less than the minimum support angle β, in the current iteration Iterative step, no reduction operation is allowed for this conformal element, to ensure that no new structures with overhang angle _βo smaller than β are generated during the iteration.

The methods of calculating the overhang virtual increase angle β _ao of the conformal element and the virtual decrease angle β _do of the conformal element are as follows:

(1) As shown in Figure 6, the gray part is the quasi-optimized conformal unit, the black unit is the outer surface unit, the vertical line filling unit is the inner surface unit of the structure, and the dashed slash filling unit is the addition of the simulated increase operation. The unit body of , fill the unit body with this oblique line as the center, and obtain the virtual increase angle β _ao of the conformal unit according to the calculation method of the overhang structure angle β _o in part (1) of step 5.

(2) As shown in Figure 7, the gray part is the to-be-optimized conformal unit, the black unit is the outer surface unit, the vertical line filled unit body is the structural inner surface unit, the gray unit with the dotted line is the unit to be removed, and the slanted line fills The element simulates the inner surface element after the reduction operation for the current conformal element, and then:

a. Make a pendant filter circle with a radius of q at the diagonal filling unit (coordinates are (x, z)).

b. Traverse the voxel units in the filter circle to find the inner surface unit body (vertical line filling unit body) with the largest distance from the center unit body (coordinates are (x, z)) in the positive direction of the Z axis (coordinates are (r, t)) .

c. Obtain the overhang angle β _do according to formula (2), where x, z, r, and t are the coordinates of the voxel unit.

S6. Set the iterative change rate l (0≤l≤0.5), and determine the iterative change number S to be obtained according to formula (4), where A is the total number of conformal units. According to the overhang function in step 5, the conformal unit with smaller p value (smaller β _o or larger h) is considered to be in the large overhang structure and needs to be removed; the conformal unit with larger p value (β _o larger or h smaller) is considered to be in a relatively small overhang and only needs to be filled. According to the number of iterative changes, the method of changing the conformal unit in step S3 is applied to the sorting queue obtained in step S4, and an increase or decrease operation is performed on the conformal unit. Perform a conformal unit reduction operation on the conformal units 0 to S in the queue sorted from small to large (except p=1); perform a conformal unit increase operation on the conformal units from (AS) to A in the queue .

S=l×A (4)

The suspension angle constraint set in step S5 is applied in the current step, and the increase and decrease operations are not performed on the constrained conformal units.

S7, reset the virtual increase and virtual decrease angle constraints for all conformal units, and re-determine in the next iteration;

S8, iterative loop from step S4 to step S7, each iteration recalculates the overhang function value according to step S4 and assigns it to the corresponding conformal unit, imposes the overhang angle constraint described in step S5 during the iteration, and changes the conformal unit according to the rule described in step S6 ; until all overhanging structure angles β _o ≥ β in the shell structure, the iteration terminates.

Figure 8 is a comparison diagram of the optimization results after applying the method when the initial overhang structure angle β _o is 30°, and the minimum self-supporting angle β is set to 45°. The optimization results show that this method can improve the internal overhang structure of the structure according to the set minimum self-support angle while keeping the outer surface topography of the structure unchanged.

The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions that belong to the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (10)

1. a shape-preserving topology optimization method considering overhang feature constraints, is characterized in that, comprises the following steps: S1. The structural model is divided into voxelized grids, and each voxel unit has its corresponding spatial coordinates; S2. Based on the voxel unit set, construct a conformal unit capable of constraining the outer surface of the structural model, and each conformal unit includes an exterior surface unit, an interior unit and an interior surface unit of the structural model; S3. Define two variations of controlling the conformal unit: the increase operation of the conformal unit and the decrease of the conformal unit; S4, define the drape function of the conformal unit, calculate the drape function value P of each conformal unit, and sort the conformal units according to the drape function value from small to large; S5. Set the minimum self-supporting angle β; obtain the virtual increase angle β _ao of the conformal element and the virtual decrease angle β _do of the conformal element; set the overhang angle constraint so that no new overhang angle β _o is generated during the iteration process Structures smaller than the minimum support angle β; S6, set the iterative change rate 1, determine the iterative change number S, apply the shape-preserving unit changing method of step S3 to the sorting queue obtained in step S4 according to the iterative change number, and perform an increase or decrease operation on the shape-preserving unit; in the current step The suspension angle constraint set in step S5 is applied, and the increase operation and decrease operation are not performed on the constrained conformal unit; S7, reset the virtual increase and virtual decrease angle constraints for all conformal units, and re-determine in the next iteration; S8. Iteratively loops steps S4 to S7 until all the overhanging structure angles β _o ≥ β on the inner surface of the structure, the iteration is terminated. 2. The shape-preserving topology optimization method as claimed in claim 1, wherein in step S2, the constructed shape-preserving unit can constrain six directions of the outer surface of the structural model, and the six directions are respectively along x, y, The positive and negative directions of the z-axis. 3. the shape-preserving topology optimization method as claimed in claim 1 is characterized in that: in step S3, the adding operation of the conformal unit is: on the inner surface side of the conformal unit, from the outer surface of the structural model to the inner surface direction, add one Voxel unit; the conformal unit reduction operation is: on the inner surface side of the conformal unit, delete one voxel unit from the inner surface to the outer surface of the structural model. 4. shape-preserving topology optimization method as claimed in claim 1, is characterized in that, the shape-preserving cell drape function defined in step S4 is as shown in formula (1), and formula (1) is as follows:

p=1( _βo≥β ) In the formula, q is the self-defined coefficient, β _o is the angle of the overhanging structure, h is the horizontal distance of the overhanging structure, and p is the overhang function value of the conformal element. 5. The shape-preserving topology optimization method as claimed in claim 4, wherein, in the x, z plane, the overhanging structure angle _β is obtained in the following manner: 1) On the inner surface unit of the conformal unit, the coordinates are (x, z) to make a pendant filter circle with a radius of q; 2) Traverse the voxel units in the filter circle, and find the inner surface unit body whose coordinates are (x, z) from the center of the circle and the largest distance in the negative direction of the Z axis, and the coordinates are (r, t); 3) Obtain the overhang angle β _o according to the formula (2), the formula (2) is as follows, and x, z, r, and t are the coordinates of the voxel unit.

6. The shape-preserving topology optimization method as claimed in claim 4, wherein, in the x, z planes, the distance h in the horizontal direction is obtained in the following manner: 1) After obtaining the overhang angle β _o of the overhanging structure where all the conformal units are located, mark the conformal units with β _o ≥ β as self-supporting units; 2) Take the inner surface unit body of the conformal unit, and the coordinates are (x, z) as the starting point to traverse along the negative direction of the Z-axis until z=0. When traversing a new line, traverse in the hanging direction of the X-axis; When a self-supporting unit is taken from the supporting unit, the coordinates are marked (a, c), and the traversal is ended; if the self-supporting unit is not traversed, the unit that is farthest from the center unit in the x direction is taken, and the coordinates are marked as (a, c); 3) Calculate the distance h in the horizontal direction according to formula (3), formula (3) is as follows, dx is the edge length of each voxel unit, and x and a are the coordinates of the voxel unit. h=|x-a|×dx 7. The shape-preserving topology optimization method as claimed in claim 1, wherein in step S5, the set overhang angle constraint is: when β _ao is less than the minimum support angle β, in the current iteration step, no shape-preserving is performed. The element performs an increase operation; when β _do is less than the minimum support angle β, in the current iteration step, no decrease operation is performed for this conformal element. 8. the shape-preserving topology optimization method as claimed in claim 5, is characterized in that, in step S5, in x, z plane, the virtual increase angle β _ao of the shape-preserving unit, the virtual decrease angle β _do of the shape-preserving unit are calculated method as follows: 1) Obtain the virtual increase angle β _ao of the conformal element according to the method for obtaining the overhang structure angle β _o ; 2) a. Simulate the inner surface unit after the reduction operation is performed in the current conformal unit, that is, the unit body at the coordinates (x, z) is the center of the circle, and a suspension filter circle with a radius of q is used; b. Traverse the voxel units in the filter circle to find the inner surface unit body with the largest distance from the center unit body in the positive direction of the Z axis, and the coordinates are (r, t); c. Obtain the overhang angle β _do according to formula (2), where x, z, r, and t are the coordinates of the voxel unit. 9. shape-preserving topology optimization method as claimed in claim 1, is characterized in that, step S6 is specifically, the smaller shape-preserving unit of the overhang function value obtained in step S5 is regarded as being in the large overhang structure, and is removed; The conformal unit with a larger dangling function value is considered to be in a small dangling structure and is filled; in the queue sorted from small to large, the conformal unit from the 0th to the S except p=1 is used to perform the conformal unit reduction operation ; Perform a conformal unit addition operation on the conformal units from (A-S)th to A in the queue, where A is the total number of conformal units. 10 . The shape-preserving topology optimization method according to claim 9 , wherein the number of iterative changes S=l×A. 11 .

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