CN112214856B - Precision machine tool rigidity optimization design method for overall structure - Google Patents
Precision machine tool rigidity optimization design method for overall structure Download PDFInfo
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Abstract
The invention relates to a precision machine tool rigidity optimization design method for an integral structure, which comprises the following steps: 1) determining the structural design space of the whole machine tool, and constructing an original entity structure needing topology; 2) setting a whole machine design optimization area and a non-design optimization area by taking the whole machine structure of the machine tool as a research object; 3) taking the whole machine structure of a machine tool as a research object, and adding loads on all stress surfaces; 4) complete machine statics analysis and complete machine dynamics analysis are adopted for the research object; 5) constructing and analyzing a topology optimization model according to the statics analysis result; 6) geometrically repairing the topological model again to ensure that the surface of the topological model has uniform grids and the surface is more uniform under the condition of keeping the original structure unchanged; 7) carrying out detail processing on the model, converting the model into a solid model, and sending the solid model to printing software for adding support; 8) and obtaining a complete machine model after the overall topology of the machine tool is optimized.
Description
Technical Field
The invention relates to a precision machine tool rigidity optimization design method, in particular to a precision machine tool rigidity optimization design method for an integral structure.
Background
The rigidity is an important target of the structural design of the precision machine tool, and the improvement of the rigidity is beneficial to improving the processing efficiency and the processing precision of the machine tool and the surface smoothness of a processed workpiece. The core problem of rigidity design in the structural design of the precision machine tool is the efficient transmission and bearing of the structure to load. The single component is subjected to dynamic and static rigidity design, so that the component structure can be changed, and the rigidity characteristic of the whole machine is improved. The best stiffness set of individual components and resulting overall structure is not equal to the best performing overall structure. Therefore, a precision machine tool rigidity optimization design method oriented to an integral structure is needed
Disclosure of Invention
In order to solve the problems, the invention provides a precision machine tool rigidity optimization design method for an overall structure.
The technical scheme of the invention is as follows: an overall structure-oriented precision machine tool rigidity optimization design method comprises the following steps:
1) determining the structural design space of the whole machine tool, and constructing an original entity structure needing topology, namely a finite element model before topology;
2) setting a whole machine design optimization area and a non-design optimization area by taking the whole machine structure of the machine tool as a research object;
3) taking the whole machine structure of the machine tool as a research object, and adding loads on all stress surfaces;
4) complete machine statics analysis and complete machine dynamics analysis are adopted for the research object;
5) constructing and analyzing a topological optimization model according to a statics analysis result, setting the weight ratio of the topological model to the weight ratio of the overall design space according to a first-order natural frequency maximum principle, and performing global search between 20% and 100% of the volume ratio to obtain a global optimal solution by the method for obtaining the maximum first-order natural frequency;
6) geometrically repairing the topological model again to ensure that the surface of the topological model is uniform in meshes and more uniform in surface under the condition of keeping the original structure unchanged, so that poor printing effect of the model due to too coarse individual curved surface of the model is avoided in model additive manufacturing;
7) carrying out detail processing on the model, converting the model into a solid model, and sending the solid model to printing software for adding support;
8) and obtaining a complete machine model after the overall topology of the machine tool is optimized.
Further, the machine tool has the following integral structure: the analysis is carried out by taking the whole structure of the machine tool as a whole instead of decomposing the machine tool structure into a plurality of parts.
Further, the complete machine statics analysis comprises: taking an original model of a machine tool as a full-solid structure, performing statics analysis and modal analysis on the model by using finite element software, dividing by adopting hexahedral meshes to obtain a complete machine finite element model of a plurality of units and a plurality of nodes, and applying load and gravity to each stress surface to obtain a stress and deformation graph under a statics condition;
further, the complete machine dynamics analysis comprises the following analysis:
a. modal analysis
Carrying out modal analysis on the whole machine to obtain the inherent frequency and the vibration mode of each order of the whole machine;
b. harmonic response analysis
In order to reflect the dynamic performance change under the excitation of different main shaft rotating speeds, a harmonic excitation force is applied to the head of a main shaft box in the X direction, the Y direction and the Z direction respectively to simulate the cutting process of a machine tool, and the excitation frequency range is 0-800 HZ;
further, the topology optimization model construction and analysis comprises:
a. variable density method topology optimization
Adopting a variable density method, namely taking the 'unit density' of each unit in the finite element model design space as a design variable, wherein the 'unit density' is related to the material parameters of the structure and is continuously valued between 0 and 1, and the unit density of 1 or close to 1 after optimization solution indicates that the material at the unit is important and needs to be reserved; the unit density is 0 or close to 0, which means that the material at the unit is unimportant and can be removed, thereby achieving the high-efficiency utilization of the material and realizing the light-weight design; through topology optimization, not only are the properties of unnecessary materials removed, but also the material distribution is more uniform, the stress is more reasonable, the force transmission efficiency is higher, and the rigidity and the inherent frequency are improved;
b. static stiffness topological optimization model
Constructing a solid isotropic material optimization model of the whole machine tool by taking the unit material density value rho as a design variable, taking the flexibility minimization as an optimization target and taking the mass difference before and after optimization as a constraint condition;
there is a non-linear relationship between the macroscopic physical quantity of the material and the density of the material
In the formula: eiIs the modulus of elasticity of unit i; mu.s0Is the initial poisson's ratio of the material; mu is Poisson's ratio；ρiIs the relative density of the cell; p is a density penalty factor, and is often taken as 3.
The mathematical model of the variable density method is as follows:
Find：ρ＝{ρ1,ρ2,ρi,...,ρn}Tε·Ω
s.t.M＝∑viηi≤M0-M1
KU＝F
0<ρm≤ρi≤1,i＝1,2,3,…,n
in the formula: rho is a unit vector of cell density; n is the number of units in the structure; c is a structural flexibility value; f is the load at the node; u is a displacement vector; k is a structural total stiffness matrix; u. ofiIs a unit i-node displacement vector; k is a radical of0Is a stiffness matrix constant; m is the reserved quality after optimization; m0Maximum mass for the initial design structure; m1Optimizing the removal quality; rhominIs the variable with the smallest relative density;
c. static stiffness optimization results
Solving by using finite element software, obtaining a retained weight W after multiple iterations, and after processing the model structure after topology, retaining the basic characteristics of the model structure and carrying out statics analysis again;
d. volume-variable modal topology optimization
Constructing a modal optimization model of the whole machine tool by taking the first-order natural frequency maximization as an optimization target and taking the front-back volume ratio, the stress maximum value and the deformation maximum value as constraint conditions:
s.t.(K-λiM){φi}＝0,i＝1,2,3,…,z
V(ρ)＝fV0
d1≤d0
σ1≤σ0
0<ρmin≤ρi≤1,i＝1,2,…,n
in the formula: lambdaiIs the corrected ith order eigenvalue; lambda [ alpha ]iThe ith order eigenvalue; omegaiThe weighted value is the corresponding weighted value of the ith order; s, lambda0Is a given parameter; k is a total stiffness matrix; m is a total mass matrix; { phiiThe feature vector corresponding to the ith order feature value is used as the feature vector; z is the total degree of freedom, where the bottom surface is fixed, three degrees of freedom are limited, i is 3; v (rho) is the total volume reserved by the whole machine after design; v0The initial volume of the whole machine tool; f is the volume ratio before and after optimization; d0Is the total deformation before topology; d1Is the total deformation after topology; sigma1Maximum stress after topology; sigma0Is the maximum value of the topological pre-stress;
e. results of modal optimization
Setting the volume ratio of the design region and the non-design region under the condition that the design region and the non-design region are not changed and other conditions are not changed, carrying out re-verification and obtaining the previous three-order modal result;
f. volume ratio and natural frequency
The obtained first-order natural frequencies are different for different volume ratios, and in the aspect of economy, the smaller the number of materials is, the better the materials are, but the maximum rigidity and the first-order natural frequency are ensured at the same time, different volume ratios are taken for modal analysis, the interval is taken as corresponding volume constraint from 20% to 100%, other conditions are consistent with those before, the first-order natural frequency is maximized in the aim, each condition is optimized, the corresponding first-order natural frequency is obtained through post-processing, the first-order natural frequencies obtained by reserving different volumes are compared, the rule is found, and an optimal result is selected.
The invention has the beneficial effects that:
the method can determine the optimized configuration of the whole structure of the precision machine tool by systematically analyzing the optimal structural arrangement scheme of the precision machine tool in the machining space.
Drawings
FIG. 1 is a flow chart of the rigidity optimization design method of the precision machine tool facing the whole structure, provided by the invention;
FIG. 2 is a space diagram of the original entity design of the whole vertical machine tool;
FIG. 3 is a schematic illustration of a non-optimized region;
FIG. 4 is a post-topology model;
FIG. 5 is a grid division diagram of the machine tool of the embodiment;
FIG. 6 is a diagram of the first three modes in the example;
wherein: (a) the vibration mode is a first-order vibration mode, (b) a second-order vibration mode, and (c) a third-order vibration mode;
FIG. 7 is a frequency amplitude response curve of a master model of a machine tool;
FIG. 8 is a plot of volume ratio versus natural frequency;
FIG. 9 is a frequency amplitude response curve of a topology optimization model;
description of reference numerals: 1. a column; 2. a main spindle box; 3. a main shaft; 4. a stress surface of the workbench; 5. a saddle bearing surface; 6. a base; 7. a multi-working condition slide rail surface; 8. a column; 9. a base; 10. a four-hinged support at the bottom surface; 11. a main spindle box; 12. a main shaft; 13. a multi-working condition slide rail surface; 14. the workbench and the slide rail stress surface.
Detailed Description
The invention is further described with reference to the following figures and examples.
As shown in fig. 1, a precision machine tool rigidity optimization design method for an overall structure includes the following steps:
1) and determining the structural design space of the whole machine tool. And constructing an original solid structure which generally needs topology, namely a topological front finite element model. For example, the original entity structure is shown in fig. 2. The original solid structure comprises a vertical column 1, a main shaft 3, a main shaft box 2, a workbench stress surface 4, a saddle stress surface 5, a base 6 and the like.
2) The whole machine structure of the machine tool is taken as a research object, and a whole machine design optimization region and a non-design optimization region are set. The plane required for mounting moving parts such as guide rails is designed as a non-design-optimized area a as shown in fig. 3.
3) The whole machine structure of the machine tool is taken as a research object, and loads are added to all stress surfaces.
4) The optimization process adopts complete machine statics analysis and complete machine dynamics analysis, including finite element method or other mechanics methods. The finite unit divides the structure into finite units, sets unit grids, calculates the transmission process of force among the units and performs statics analysis.
5) And constructing and analyzing a topological optimization model according to the static analysis result, and setting the weight ratio of the weight of the topological model to the weight of the whole design space according to the first-order natural frequency maximum principle. The method for obtaining the maximum first-order natural frequency is to perform global search between 0% and 100% to obtain a global optimal solution. For example, the weight of the topology model in the present embodiment is 32% of the weight of the entire design space. The topological back model, as shown in fig. 4, includes a multi-condition slide rail surface 7, a column 8, a base 9, a bottom four-hinged support 10, a spindle box 11, a spindle 12, a multi-condition slide rail surface 13, a workbench and a slide rail stress surface 14.
6) And geometrically repairing the post-topological model again. The method mainly carries out grid repairing to ensure that the grids on the surface of the topological model are uniform, so that the surface of the model is more uniform under the condition that the original structure is kept unchanged. Ensure that the additive manufacturing of the model can not lead to poor printing effect of the model because the individual curved surface of the model is too rough.
7) And carrying out detail processing on the model to obtain a satisfactory model, converting the model into a solid model, sending the solid model to printing software for adding support, and adding support.
8) The invention relates to a method for designing a machine tool structure, which is the overall topological design of a machine tool. And obtaining a complete machine model after topology optimization.
In the examples:
(1) complete machine statics analysis
Using the original model of the machine tool, the model being a full solid knotAnd (5) forming. The height of the basic parameters is 1550mm, the length is 1300mm, and the thickness of the base is 350 mm. Performing statics analysis and modal analysis on the model by using ANSYS Workbench, wherein the model is made of cast iron and the density of the material is rho 7.2 multiplied by 103kg/m3The elastic modulus E is 110GPa, and the Poisson's ratio mu is 0.28. Since the model is an originally designed entity model, many fine structures are ignored. The hexahedral mesh is adopted for division to obtain a complete machine finite element model with 96449 units and 402054 nodes, as shown in fig. 5, stress and deformation graphs under the static condition can be obtained after load gravity is applied to each stress surface, the maximum value of the stress is 44.764MPa, and the maximum deformation is 0.6085 mm.
(2) Complete machine dynamics analysis
a. Modal analysis
The modal analysis is the basic content of the structural dynamics analysis and is also the premise of other dynamics analysis. The modal analysis of the whole machine can obtain the natural frequency and the mode shape of each order of the whole machine. The natural frequencies and the mode shapes of the respective orders are shown in Table 1, and the first three mode shapes are shown in (a), (b) and (c) of FIG. 6.
TABLE 1 front 6 order modal frequency of machine tool
b. Harmonic response analysis
In order to reflect the dynamic performance change under the excitation of different main shaft rotating speeds, 2000N of simple harmonic excitation force is applied to the head of the main shaft box in the X direction, the Y direction and the Z direction respectively to simulate the cutting process of a machine tool, and the excitation frequency range is 0-500 HZ. As can be seen from fig. 7, the frequency amplitude is maximum in the X direction at about 76HZ, and peaks appear in the Y direction and the Z direction. The first order mode 76.223HZ is illustrated as the first order natural frequency of this model.
3) Topology optimization model construction and analysis
a. Variable density method topology optimization
Topological optimization is one of three optimization modes, is mainly used for optimal layout of a material structure, and is widely applied to lightweight design of various product structures. The topological optimization can not only remove the properties of unnecessary materials, but also enable the material distribution to be more uniform, the stress to be more reasonable and the transmission efficiency of the force to be higher, thereby improving the rigidity, the inherent frequency and the like of the device.
The topology optimization mainly comprises a homogenization method, a variable density method, a structure asymptotic optimization method and the like. The variable Density method is used here, i.e. the "Density of elements (Density)" of each element of the finite element model design space is used as a design variable. The unit density is related to the material parameters of the structure, the values are continuously taken between 0 and 1, and the unit density of 1 (or close to 1) after the optimization solution indicates that the material at the unit is important and needs to be reserved; a cell density of 0 (or close to 0) means that the material at the cell is not important and can be removed, thereby achieving high efficiency of material utilization and achieving a lightweight design. In essence, the structural topology optimization problem based on the variable density method is a discrete optimization problem comprising the increase and decrease of units. The first-order natural frequency problem of the rigidity and the mode is considered, namely the integral rigidity characteristic and the first-order natural frequency are improved under the condition that a certain volume ratio is determined.
b. Static stiffness topological optimization model
In order to design the whole machine model with enough rigidity to overcome the stress and deformation generated by the machine tool during working and end the material, the force transmission is more efficient, and the material distribution is more reasonable. And (3) constructing a solid isotropic material optimization model of the whole machine tool by taking the unit material density value rho as a design variable, taking the flexibility minimization as an optimization target and taking the mass difference before and after optimization as a constraint condition.
There is a non-linear relationship between the macroscopic physical quantity of the material and the density of the material
In the formula: eiIs the elastic modulus of unit i; mu.s0Is the initial poisson's ratio of the material; mu is Poisson's ratio; rhoiIs the relative density of the cell; p is a density penalty factor, oftenTake p as 3.
The mathematical model of the variable density method is as follows
Find：ρ＝{ρ1,ρ2,ρi,...,ρn}Tε·Ω
s.t.M＝∑viηi≤M0-M1
KU＝F
0<ρm≤ρi≤1,i＝1,2,3,…,n
In the formula: rho is a unit vector of cell density; n is the number of units in the structure; c is a structural flexibility value; f is the load at the node; u is a displacement vector; k is a structural total stiffness matrix; u. ofiIs a unit i-node displacement vector; k is a radical of0Is a stiffness matrix constant; m is the reserved quality after optimization; m0Maximum mass for the initial design structure; m1Optimizing the removal quality; rhominIs the variable with the smallest relative density.
c. Static stiffness optimization results
And (3) solving by using ANSYS Workbench, and obtaining the retained weight W which is 41 percent of the original model after 29 iterations. The structure after topology is processed, and the basic characteristics are kept to carry out statics analysis again.
Comparing various parameters of the original structure before topology and the model after topology, as shown in table 2, the original deformation is 0.6085mm according to the result, and the deformation is 0.4586mm after topology optimization, so that the integral rigidity can be judged to be increased. The overall mass decreased from 5135.5kg to 2088.6kg, a significant improvement in material distribution.
TABLE 2 deformation and quality parameter table before and after optimization
d. Volume-variable modal topology optimization
The modal topology optimization mainly improves the low-order natural frequency of the structure, and the low-order natural frequency is easy to generate a resonance phenomenon when being excited by the outside, so that the first-order natural frequency of the whole machine tool is improved as much as possible under the condition that other working conditions are met. In topology optimization, different volume ratios are reserved after topology is found, natural frequencies of the topology and the volume ratios are different, and under the maximum constraint of a certain volume ratio, the first-order natural frequency increases along with the increase of the volume and finally approaches to a certain stable value. The first-order natural frequency maximization is taken as an optimization target, and a modal optimization model of the whole machine tool is constructed by taking the front-back volume ratio, the maximum stress value and the maximum deformation value as constraint conditions.
s.t.(K-λiM){φi}＝0,i＝1,2,3,…,z
V(ρ)＝fV0
d1≤d0
σ1≤σ0
0<ρmin≤ρi≤1,i＝1,2,…,n
In the formula: lambdaiIs the corrected ith order eigenvalue; lambda [ alpha ]iThe ith order eigenvalue; omegaiThe weighted value is the corresponding weighted value of the ith order; s, lambda0Is a given parameter; k is a total stiffness matrix; m is a total mass matrix; { phiiThe feature vector corresponding to the ith order feature value is used as the feature vector; z is the total degree of freedom, where the bottom surface is fixed, three degrees of freedom are limited, i is 3; v (rho) is the total volume reserved by the whole machine after design; v0The initial volume of the whole machine tool; f is the volume ratio before and after optimization; d0Is the total deformation before topology; d1Is the total post-topological deformation; sigma1Maximum stress after topology; sigma0Is the maximum value of the topological pre-stress.
e. Results of modal optimization
The volume ratio f was set to 28% with the design area unchanged from the non-design area and with the other conditions unchanged, and the result was 31%. And the previous three-order modal result is obtained through re-verification of the result, namely on the premise that the maximum stress is 44.764MPa and the maximum deformation is 0.6085 mm. And comparing the first-order natural frequency, the quality and the like of the original model and the optimized model before and after optimization. As shown in table 3.
TABLE 3 topological front and back order natural frequency parameter table
Through optimization, the first-order natural frequency of the whole machine tool is obviously improved to a great extent, the lifting rate is 62.195% when the first-order natural frequency is lifted to 123.63HZ from 76.223HZ, the machine tool is obviously improved in working, and the quality of the machine tool is also reduced from 5135.5kg to 1598.7 kg.
f. Volume ratio and natural frequency
The first order natural frequency is different for different volume ratios, but from an economic point of view, it is of course better to have fewer materials, but at the same time to ensure that the stiffness and the first order natural frequency are at their maximum. The volume ratio is limited below 45%, different volume ratios are selected for modal analysis, each 1% interval is used as corresponding volume constraint from 20% to 100%, other conditions are consistent with those of the previous cases, the first-order natural frequency is maximized in the aim, each case is optimized, the corresponding first-order natural frequency is obtained through post-processing, the first-order natural frequencies obtained by reserving different volumes are compared, the rule is found, and an optimal result is selected.
The first-order natural frequency corresponding to each volume ratio is obtained by performing topology iteration on the condition of each volume ratio, as shown in fig. 8, the natural frequencies corresponding to different volume constraints are clearly expressed. Through the iteration results of different volume ratios, the natural frequency is small at the beginning and is increased along with the increase of the volume ratio, the first-order natural frequency is basically maintained at a stable value in a certain range, and then the first-order natural frequency is continuously reduced to the first-order natural frequency value of the original model along with the increase of the volume ratio. Therefore, considering that the first order natural frequency is the largest, the retention volume ratio of 32% or more is about 124.45HZ, and considering economic benefits such as materials, the less the material, the better, the best result is obtained when the volume ratio is 32%. The first-order natural frequency is 124.45HZ, and the increase is 63.27% compared with the original entity model 76.223 HZ. The weight of the human body is reduced from 5135.5kg to 1652.3 kg. FIG. 9 is a frequency amplitude response curve of a topology optimization model. g. Comparison of prototype machine tool with topology optimization machine tool
The method is characterized in that the same prototype machine tool is compared with the first 6-order mode of a topological machine tool, analysis is carried out after simplification of the prototype machine tool, the whole machine tool is an assembly body formed by all parts, the topological optimization model is that the prototype machine tool is regarded as a whole, part contacts of the prototype machine tool are all set to be binding contacts, the degrees of freedom of all parts of the prototype machine tool are bound together to form a whole, and modal and statics analysis is carried out. The results of comparison are shown in Table 4.
TABLE 4 comparison of prototype machine tool with topological post-machine tool mode
As can be seen from the comparison between the prototype machine tool and the machine tool model after topology optimization in the first 6 th order mode in table 4, the frequency of the model obtained by topology optimization is higher than that of the prototype machine tool.
The method adopts additive manufacturing and experimental verification:
(1) additive manufacturing
The topological optimization is a design method for reasonably distributing materials according to formulated load working conditions, performance indexes and constraint conditions so as to determine the optimal force transmission path strength of the structure. Although this method can reasonably reduce materials and improve performance, the topologically optimized structure often has a complex geometric configuration, and the traditional manufacturing technology (such as machining, casting, etc.) is difficult to prepare, so that secondary manufacturing needs to be performed on the basis of considering the difficulty and the manufacturability, and the advantage of topology optimization cannot be exerted. Thus, other manufacturing methods need to be considered.
The advent of Additive Manufacturing (Additive Manufacturing) technology has facilitated topological optimization models as well as other complex models. The technology is used for manufacturing an object structure in a layer-by-layer material accumulation mode, and has wide applicability, particularly stronger applicability to objects with complex structural configurations. The additive manufacturing technology is developed in decades, is mature, not only has high production efficiency in small-batch production, but also can fully exert the advantage of topological optimization, and enables the structural performance and the material distribution to be more reasonable.
In the embodiment, a series of analyses are carried out to obtain a model of the first-order maximum natural frequency under the condition that the rigidity, the deformation and the maximum equivalent stress are guaranteed to be upper limits, the model is subjected to post-processing and printed by using an additive technology. The size and the size of the model after the original topology are large, the printing equipment and the capital are not particularly sufficient under the condition of considering the cost, and the model is reduced to 1:10 in proportion. Due to the existing additive technology, the material is not particularly sufficient, and the difficulty is different. The analysis of the original model is the result obtained by analyzing cast iron as a material, and two materials in the aspect of metal can be stainless steel and aluminum alloy. The properties of the stainless steel material were determined to be higher and closer to cast iron when comparing the two material properties, where 3D printing additive manufacturing was performed using stainless steel as the starting material. And (4) analyzing again under the condition that the material is stainless steel to obtain the deformation, the stress and the first three-order modal frequency. Maximum equivalent is 5.0367 MPa; the overall deformation is 0.0032364 mm; the maximum strain is 3.1537e-5 mm. The first three-order modal frequencies are 1578.4HZ respectively; 1709.2 HZ; 2510.3 HZ.
Before additive manufacturing, a series of operations such as post-processing and smoothing are required to be carried out on a model, and finally the model with a smooth surface and a reasonable structure is obtained, so that 3D printing is started, firstly, support is added to the model, a support structure is added from the side, then additive manufacturing is started, and the model is printed by adopting an EOS M280-SLM metal 3D printer. After the printed pattern is obtained, it is subjected to support removal, heat treatment, grinding, polishing, sand blasting to obtain the final product. Heat treatment is essential for the manufacture of metal models, the function of which is to improve the mechanical properties of the material, to eliminate residual stresses and to improve the machinability of the metal, which is a good improvement in the properties of the product.
Claims (2)
1. An optimal design method for the rigidity of a precision machine tool facing to an integral structure is characterized by comprising the following steps:
1) determining the structural design space of the whole machine tool, and constructing an original entity structure needing topology, namely a finite element model before topology;
2) setting a whole machine design optimization area and a non-design optimization area by taking the whole machine structure of the machine tool as a research object;
3) taking the whole machine structure of the machine tool as a research object, and adding loads on all stress surfaces;
4) complete machine statics analysis and complete machine dynamics analysis are adopted for the research object;
the complete machine statics analysis comprises the following steps: taking a machine tool original model as a full-solid structure, performing statics analysis and modal analysis on the model by using finite element analysis software, dividing by adopting hexahedral meshes to obtain a complete machine finite element model of a plurality of units and a plurality of nodes, and applying load and gravity to each stress surface to obtain a stress and deformation graph under a statics condition;
the complete machine dynamics analysis comprises the following analysis:
a. modal analysis
Carrying out modal analysis on the whole machine to obtain the inherent frequency and the mode shape of each order of the whole machine;
b. harmonic response analysis
In order to reflect the dynamic performance change under the excitation of different main shaft rotating speeds, simple harmonic excitation force is applied to the head of a main shaft box in the X direction, the Y direction and the Z direction respectively to simulate the cutting process of a machine tool, the excitation frequency range is 0-800 HZ, the maximum amplitude values in the X direction, the Y direction and the Z direction within the frequency range are obtained and compared, and the first-order inherent frequency is judged;
5) constructing and analyzing a topological optimization model according to a statics analysis result, setting the volume ratio of the volume of the topological model to the volume of the whole design space according to a first-order natural frequency maximum principle, and performing global search between 20% and 100% of the volume ratio to obtain a global optimal solution by the method for obtaining the maximum first-order natural frequency;
the topology optimization model construction and analysis comprises the following steps:
a. topology optimization by variable density method
Adopting a variable density method, namely taking the unit density of each unit in the finite element model design space as a design variable, wherein the unit density is related to the material parameters of the structure, and values are continuously taken between 0 and 1, and the unit density of 1 or close to 1 after optimization solution represents that the material at the unit is important and needs to be reserved; the unit density is 0 or close to 0, which means that the material at the unit is unimportant and can be removed, thereby achieving the high-efficiency utilization of the material and realizing the light-weight design; through topology optimization, not only are unnecessary material attributes removed, but also material distribution is more uniform, stress is more reasonable, force transmission efficiency is higher, and therefore rigidity and inherent frequency are improved;
b. static stiffness topological optimization model
Constructing a solid isotropic material optimization model of the whole machine tool by taking the unit material density value rho as a design variable, taking the flexibility minimization as an optimization target and taking the mass difference before and after optimization as a constraint condition;
there is a non-linear relationship between the macroscopic physical quantity of the material and the density of the material
In the formula: eiIs the elastic modulus of unit i; mu.s0Is the initial poisson's ratio of the material; mu is Poisson's ratio; rhoiIs the relative density of the cell; p is a density penalty factor, and is usually taken as 3;
the mathematical model of the variable density method is as follows:
Find：ρ＝{ρ1,ρ2,ρi,...,ρn}Tε·Ω
Min：
s.t. M＝∑viηi≤M0-M1
KU＝F
0<ρm≤ρi≤1,i＝1,2,3,…,n
in the formula: rho is a unit vector of cell density; n is the number of units in the structure; c is a structural flexibility value; f is the load at the node; u is a displacement vector; k is a structural total stiffness matrix; u. ofiIs a unit i-node displacement vector; k is a radical of0Is a stiffness matrix constant; m is the reserved quality after optimization; m0Maximum mass for the initial design structure; m1Optimizing the removal quality; ρ is a unit of a gradientminIs the variable with the smallest relative density;
c. static stiffness optimization results
Solving by using finite element software, obtaining a retained weight W after multiple iterations, and after processing the model structure after topology, retaining the basic characteristics of the model structure and carrying out statics analysis again on the model structure;
d. volume-variable modal topology optimization
Constructing a modal optimization model of the whole machine tool by taking the first-order natural frequency maximization as an optimization target and taking the front-back volume ratio, the stress maximum value and the deformation maximum value as constraint conditions:
s.t. (K-λiM){φi}＝0,i＝1,2,3,…,z
V(ρ)＝fV0
d1≤d0
σ1≤σ0
0<ρmin≤ρi≤1,i＝1,2,…,n
in the formula: lambdaiIs the corrected ith order eigenvalue; lambda [ alpha ]iThe ith order eigenvalue; omegaiThe weighted value is the corresponding weighted value of the ith order; s, lambda0Is a given parameter; k is a total stiffness matrix; m is a total mass matrix; { phiiThe feature vector corresponding to the ith order feature value is used as the feature vector; z is the total degree of freedom, where the bottom surface is fixed, three degrees of freedom are limited, i is 3; v (rho) is the total volume reserved by the whole machine after design; v0The initial volume of the whole machine tool; f is the volume ratio before and after optimization; d is a radical of0Is the total deformation before topology; d1Is the total post-topological deformation; sigma1Maximum stress after topology; sigma0Is the maximum value of the topological pre-stress;
e. results of modal optimization
Setting the volume ratio of the design region and the non-design region under the condition that the other conditions are not changed, carrying out re-verification and obtaining the modal result of the first three orders;
f. volume ratio and natural frequency
For different volume ratios, the obtained first-order natural frequencies are different, and from the economic aspect, the smaller the number of materials is, the better the first-order natural frequency is, but the maximum rigidity and the first-order natural frequency are also ensured, other conditions are consistent with those of the prior art, the first-order natural frequency is maximized in the aim, each condition is optimized, the corresponding first-order natural frequency is obtained through post-processing, the first-order natural frequencies obtained by keeping different volumes are compared, the rule is found, and an optimal result is selected;
6) geometrically repairing the topological model again to ensure that the surface of the topological model is uniform in meshes and more uniform in surface under the condition of keeping the original structure unchanged, so that poor printing effect of the model due to too coarse individual curved surface of the model is avoided in model additive manufacturing;
7) carrying out detail processing on the model, converting the model into a solid model, and sending the solid model to printing software for adding support;
8) and obtaining a complete machine model after the overall topology of the machine tool is optimized.
2. The rigidity optimization design method for the precision machine tool facing the whole structure is characterized in that the rigidity optimization design method for the whole structure of the machine tool is as follows: the analysis is carried out by taking the whole structure of the machine tool as a whole instead of decomposing the machine tool structure into a plurality of parts.
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