Method for optimizing design and manufacture of self-supporting structure based on multi-axis 3d printing

A method for optimizing design and manufacture of a self-supporting structure based on multi-axis 3D printing, which comprises the following steps:

• S1, topology optimization without overhanging constraints:
• using a structural topology optimization method based on an SIMP model to realize the optimal configuration design of a complex structure, converting an image into a binary image, and post-processing a result of the topology optimization;
• S2, multi-axis 3D partition printing optimization:
• first, extracting a structural boundary, determining an overhanging angle of the structure boundary, dividing the structure into printing partitions, classifying the printing partitions, determining the printing direction of different printing partitions according to classification;
• and performing integrated optimization of angle constraints;
• wherein, step S2 specifically comprises:
• S2.1, determining the overhanging angle of the structural boundary:
• inputting the binary image obtained in step S1 in a matrix form to obtain density values in a neighborhood of each unit;
• if the density in the neighborhood of a unit is 0, the unit is a boundary unit;
• fitting the unit density of the boundary unit without binarization processing in the neighborhood to obtain a gradient normal vector of the boundary unit, and taking the orthogonal direction of the gradient normal vector as the boundary overhanging direction;
• and using a least square method to fit the unit density in the neighborhood to obtain the gradient direction of the unit density;
• each unit supporting domain is divided by a six-unit mode or a nine-unit mode, each unit supporting domain is divided into a left supporting domain and a right supporting domain, normal vectors of a left boundary and a right boundary of the structure are obtained by fitting the unit density by the least square method, respectively, and the normal vectors of the left boundary and the right boundary are inner-producted with the structural molding direction, respectively, so as to obtain a magnitude of the left boundary and the right boundary of the structure violating a critical overhanging angle:
• {
• t
• il
• =
• (
• cos
• ⁢
• α
• l
• -
• cos
• ⁢
• α
• _
• )
• ⁢
• 
• ∇
• ρ
• ~
• l
• 
• ≤
• ε
• i
• ⁢
• 1
• t
• ir
• =
• (
• cos
• ⁢
• α
• r
• -
• cos
• ⁢
• α
• _
• )
• ⁢
• 
• ∇
• ρ
• ~
• r
• 
• ≤
• ε
• i
• ⁢
• 1
• ,
• i
• =
• 1
• ,
• TagBox[",", "NumberComma", Rule[SyntaxForm, "0"]]
• 2
• ,
• …
• ,
• nele
• where cosαl and cosαr are cosine values of the normal vectors of the left boundary and the right boundary of the structure, respectively;
• cos α is a cosine of the critical overhanging angle of the structure;
• ∇{tilde over (ρ)} l and ∇{tilde over (ρ)} r are gradient normal vectors of the left boundary and the right boundary of the structure, respectively;
• εi1 is the parameter approaching 0 and used to avoid numerical problems;
• til and tir are magnitudes of the left boundary and the right boundary violating the critical overhanging angle, respectively, til and tir are processed by a penalty function and converted into discrete values in the range of 0-1,
• h
• ⁡
• (
• x
• )
• =
• 1
• 1
• +
• e
• -
• μ
• ⁢
• x
• where μ represents the smoothness of a function curve, μ has a value between 65 and 95, a parameter value A, characterizing the overhanging angle of the unit is as follows:
• λi=h(til−εil)·h(tir−εir)
• when the unit violates the critical overhanging angle of the structure, the value of A, is 1, otherwise the value is 0, that is:
• λ
• i
• =
• {
• 0
• ,
• t
• i
• ⁢
• l
• -
• ε
• i
• ⁢
• 1
• ≤
• 0
• ⁢
• or
• ⁢
• t
• ir
• -
• ε
• i
• ⁢
• 1
• ≤
• 0
• 1
• ,
• others
• ;
• S2.2, determining the direction of the partition printing:
• extracting graphic feature points, dividing a grid using the feature points to discretize the design domain, obtaining different printing partitions, classifying the printing partitions according to the classification of the units contained in the printing partitions, and determining the printing directions of different partitions, respectively;
• S2.3, integrated optimization of angle constraints:
• performing angle constraints on the units in each partition according to local printing directions of the structure determined in step S2.2 and realizing supplementary optimization design and printing of an insufficiently printed area;
• S3, 3D printing integrated manufacturing:
• extracting structural information through optimization results, establishing a 3D solid model by a process of assembling components and generating nodes, partitioning and slicing the solid model, and generating a printing path for self-supporting multi-axis 3D printing manufacturing.