CN117172043A - Design method for integrating dimension parameters and topological structure of robot - Google Patents
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Abstract
The invention discloses a design method for integrating a robot scale parameter and a topological structure, which comprises the following steps: determining the mechanism type of the robot, and selecting a mathematical tool; establishing a kinematic model and a working space model of a mechanism; establishing a rigidity model of the mechanism; determining working space, rigidity and performance indexes which need to be met by the robot; establishing a performance index model of the mechanism; determining a size parameter range of each component in the mechanism based on the working space; determining the section parameter range of each component in the mechanism based on the quality requirement in the performance index and the model of the standard component; carrying out mechanism stress analysis to determine a component needing topology optimization; performing topology optimization on the determined components; carrying out topology structure processing; establishing a rigidity-quality meta-model; and (3) performing optimal design to generate a topological structure, and obtaining the optimal scale parameters and the topological structure of the mechanism. The method solves the problem of mutual fracture of topological structure design and scale design, and has excellent optimization capability.
Description
Technical Field
The invention belongs to the technical field of performance design of robots, and particularly relates to a design method for integrating dimension parameters and topological structures of robots.
Background
The performance design is a key link of autonomous development and engineering application of the robot, and the structure and the scale of each part of the robot are required to be designed according to the application environment of the robot, so that the performance design is a nonlinear optimization problem with multiple targets, multiple parameters and multiple constraints.
Although the existing multi-objective optimization design methods such as a weight coefficient method, a constraint conversion method, a Pareto front edge method and the like can be utilized, the existing method for optimizing the topological structure of the robot part mainly focuses on the light-weight design after parameterization design, and the method for simultaneously optimizing the dimensional parameter and the topological structure design respectively only optimizes the dimensional parameter of the robot part under a single topological structure, does not really reveal the action rule between the dimensional parameter and the topological structure, and can not lead to the fact that the machine humanization can not reach theoretical optimal;
at the same time, the topology is typically manually trimmed to meet manufacturing manufacturability, with the process results depending on the designer's experience.
Therefore, how to develop performance design with synchronous optimization of robot scale parameters and topology and standardized manufacturing process is still a problem to be solved.
Disclosure of Invention
The invention provides a design method for integrating dimension parameters and a topological structure of a robot, which aims to solve the problems existing in the prior art.
The technical scheme of the invention is as follows: a design method for integrating robot scale parameters and topological structures comprises the following steps:
A. determining a mechanism type of the robot, and selecting a mathematical tool according to the mechanism type;
B. establishing a kinematic model and a working space model of a mechanism;
C. establishing a rigidity model of the mechanism;
D. according to the application scene of the robot, determining working space, rigidity and performance indexes which need to be met by the robot;
E. establishing a performance index model of the mechanism;
F. determining a size parameter range of each component in the mechanism based on the working space;
G. determining the section parameter range of each component in the mechanism based on the quality requirement in the performance index and the model of the standard component;
H. carrying out mechanism stress analysis to determine a component needing topology optimization;
I. performing topology optimization on the determined components;
J. carrying out topology structure processing;
K. establishing a rigidity-quality meta-model;
and L, carrying out optimal design to generate a topological structure, and obtaining the optimal scale parameters and the topological structure of the mechanism.
Further, step a determines the mechanism type of the robot, and selects a mathematical tool for the mechanism type, and the specific process is as follows:
firstly, judging whether a closed loop branched chain exists in a mechanism;
then judging whether a serial structure exists in the mechanism or not;
then, determining whether the mechanism is a serial mechanism, a parallel mechanism or a series-parallel mechanism;
finally, a corresponding mathematical tool is selected according to the type of the mechanism.
Furthermore, the step B establishes a kinematic model and a working space model of the mechanism, and the specific process is as follows:
firstly, solving a kinematic forward and inverse solution of a mechanism based on the obtained mechanism type and a selected mathematical tool;
and then, establishing and obtaining the working space constraint of the mechanism according to the obtained forward and reverse solutions.
Furthermore, the stiffness model of the mechanism is built in the step C, and the specific process is as follows:
firstly, obtaining a kinematic model based on the step B, and establishing a force rotation space and a motion rotation space of a mechanism;
and then obtaining the rigidity connection relation of each module of the mechanism according to the serial-parallel characteristics of the mechanism.
Further, step D determines working space, rigidity and performance indexes to be satisfied by the robot according to an application scenario of the robot, and the specific process is as follows:
firstly, determining an application scene of a robot to obtain application scene requirements;
and then, according to the specific application scene requirements, determining the working space, the rigidity requirement and the performance index of the tail end of the mechanism.
Furthermore, the topology optimization is carried out on the determined components in the step I, and the specific process is as follows:
firstly, combining scale parameters by using an orthogonal experiment method;
then, according to the combination result, obtaining components with different specifications under different combination conditions;
and then, carrying out topological optimization on the component to be optimized by utilizing finite element software.
Furthermore, the topology workability treatment is performed in the step J, and the specific process is as follows:
firstly, establishing a standardized processing algorithm which enables a topological structure to meet manufacturing manufacturability;
then, a topology conforming to manufacturing manufacturability is normalized using a workability processing algorithm based on edge detection.
Furthermore, the stiffness-mass meta-model is built in the step K, and the specific process is as follows:
firstly, extracting the rigidity of each component by means of FEA software;
then, constructing the mapping of each component scale parameter and the rigidity and the quality of each component scale parameter by using RSM;
finally, a stiffness-mass meta-model of the topology optimization component is formed.
Furthermore, the step L is optimized to generate a topological structure, and the optimal scale parameters and the topological structure of the mechanism are obtained, and the specific process is as follows:
firstly, embedding all obtained component rigidity-mass element models into a robot complete machine rigidity model and a mass model;
then, solving by adopting an optimization algorithm to obtain a Pareto front by using the determined optimization target;
and finally, selecting an optimal result from the Pareto front according to the cooperative balance point criterion, thereby obtaining the optimal scale parameter and the topological structure of the mechanism.
Further, the determined optimization targets are as follows:
and D, taking the maximum rigidity as a target, the minimum mass as a target and taking the performance index determined in the step D as an optimization target.
The beneficial effects of the invention are as follows:
the method establishes algebraic relation of the topological structure, the scale and the performance of the mechanism, comprehensively considers the coupling influence rule of the topological structure and the scale on the performance, solves the problem of mutual fracture of topological structure design and scale design, and has excellent optimizing capability.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a flow chart of a performance design method for synchronous optimization of robot scale parameters and topology in the present invention;
FIG. 3 is a schematic diagram of collaborative equalization criteria in the present invention;
FIG. 4 is a diagram depicting a coordinate system in an embodiment of the invention;
FIG. 5 is a diagram of a workability treatment in an embodiment of the present invention;
fig. 6 is a diagram of the initial topology versus the final topology in an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the drawings and examples:
as shown in fig. 1 to 3, a design method for integrating a dimension parameter and a topological structure of a robot includes the following steps:
A. determining a mechanism type of the robot, and selecting a mathematical tool according to the mechanism type;
B. establishing a kinematic model and a working space model of a mechanism;
C. establishing a rigidity model of the mechanism;
D. according to the application scene of the robot, determining working space, rigidity and performance indexes which need to be met by the robot;
E. establishing a performance index model of the mechanism;
F. determining a size parameter range of each component in the mechanism based on the working space;
G. determining the section parameter range of each component in the mechanism based on the quality requirement in the performance index and the model of the standard component;
H. carrying out mechanism stress analysis to determine a component needing topology optimization;
I. performing topology optimization on the determined components;
J. carrying out topology structure processing;
K. establishing a rigidity-quality meta-model;
and L, carrying out optimal design to generate a topological structure, and obtaining the optimal scale parameters and the topological structure of the mechanism.
Step A, determining the mechanism type of the robot, and selecting a mathematical tool according to the mechanism type, wherein the specific process is as follows:
firstly, judging whether a closed loop branched chain exists in a mechanism;
then judging whether a serial structure exists in the mechanism or not;
then, determining whether the mechanism is a serial mechanism, a parallel mechanism or a series-parallel mechanism;
finally, a corresponding mathematical tool is selected according to the type of the mechanism.
And B, establishing a kinematic model and a working space model of the mechanism, wherein the specific process is as follows:
firstly, solving a kinematic forward and inverse solution of a mechanism based on the obtained mechanism type and a selected mathematical tool;
and then, establishing and obtaining the working space constraint of the mechanism according to the obtained forward and reverse solutions.
And C, establishing a rigidity model of the mechanism, wherein the specific process is as follows:
firstly, obtaining a kinematic model based on the step B, and establishing a force rotation space and a motion rotation space of a mechanism;
and then obtaining the rigidity connection relation of each module of the mechanism according to the serial-parallel characteristics of the mechanism.
Step D, according to the application scene of the robot, determining the working space, rigidity and performance indexes which the robot needs to meet, wherein the specific process is as follows:
firstly, determining an application scene of a robot to obtain application scene requirements;
and then, according to the specific application scene requirements, determining the working space, the rigidity requirement and the performance index of the tail end of the mechanism.
And step I, performing topology optimization on the determined components, wherein the specific process is as follows:
firstly, combining scale parameters by using an orthogonal experiment method;
then, according to the combination result, obtaining components with different specifications under different combination conditions;
and then, carrying out topological optimization on the component to be optimized by utilizing finite element software.
And (C) carrying out topology structure processability treatment, wherein the specific process is as follows:
firstly, establishing a standardized processing algorithm which enables a topological structure to meet manufacturing manufacturability;
then, a topology conforming to manufacturing manufacturability is normalized using a workability processing algorithm based on edge detection.
And (K) establishing a rigidity-quality meta-model, wherein the specific process is as follows:
firstly, extracting the rigidity of each component by means of FEA software;
then, constructing the mapping of each component scale parameter and the rigidity and the quality of each component scale parameter by using RSM;
finally, a stiffness-mass meta-model of the topology optimization component is formed.
And step L, carrying out optimal design to generate a topological structure, and obtaining optimal scale parameters and the topological structure of the mechanism, wherein the specific process is as follows:
firstly, embedding all obtained component rigidity-mass element models into a robot complete machine rigidity model and a mass model;
then, solving by adopting an optimization algorithm to obtain a Pareto front by using the determined optimization target;
and finally, selecting an optimal result from the Pareto front according to the cooperative balance point criterion, thereby obtaining the optimal scale parameter and the topological structure of the mechanism.
The specific target of the determined optimization target is as follows:
and D, taking the maximum rigidity as a target, the minimum mass as a target and taking the performance index determined in the step D as an optimization target.
Specifically, step a determines the mechanism type of the robot, and selects a mathematical tool for the mechanism type, and the process of selecting the mathematical tool is as follows:
firstly, a serial mechanism generally adopts mathematical tools common in the fields of DH method, POE method and the like;
then, the parallel mechanism and the series-parallel mechanism generally adopt common mathematical tools such as instantaneous rotation, limited rotation, closed-loop vector method, geometric method and the like.
In the presence of parallel tools, the choice of mathematical tools is determined by the developer based on the institutional characteristics and experience,
specifically, the step B is to build a kinematic model and a working space model of the mechanism, and the specific process is as follows:
firstly, solving a kinematic forward and inverse solution of a mechanism based on the obtained mechanism type and a selected mathematical tool;
then, according to the obtained forward and reverse solutions, establishing and obtaining the working space constraint of the mechanism, wherein the working space constraint is specifically expressed as follows:
in θ l,i ，l i And D l,i Respectively represent the rotating joint stroke, the moving joint stroke and the branched chain stemDistance involved.
The method is more specifically described for a series mechanism, a parallel mechanism and a series-parallel mechanism:
firstly, solving a complex series-parallel mechanism for the series mechanism and partial kinematic inverse solution, and obtaining the working space of the mechanism, wherein the working space of the mechanism is specifically as follows:
firstly, determining random points of a large number of driving joints by adopting a Monte Carlo method;
then, calculating a large number of mechanism end points meeting the constraint of the working space through a kinematic positive solution algorithm to obtain the working space of the mechanism.
Secondly, solving a complex series-parallel mechanism for the parallel mechanism and part of kinematic forward solution, and obtaining a working space of the mechanism, wherein the working space is specifically as follows:
firstly, searching end point coordinates of a mechanism in a Cartesian space according to a searching step length set by a research staff according to experience by adopting a limit searching method;
then, calculating the rotation and movement joint travel of the mechanism through a kinematic inverse solution algorithm, calculating the pose and interference distance of each branched chain, and carrying out working space constraint judgment;
and finally, reserving the end points of the mechanism meeting the constraint to obtain the working space of the mechanism.
Specifically, the stiffness model of the mechanism is built in the step C, and the stiffness model is specifically as follows:
first, based on a kinematic model, a force rotation space and a motion rotation space of a mechanism are established.
More specifically, according to the serial-parallel characteristics of the mechanism, the rigidity connection relation of each module of the mechanism is obtained;
the stiffness of the series of modules is the inverse of the stack of their compliance
K＝(C L1 +C L2 +C L3 ) -1 (2)
Wherein C is Li Compliance for each series module
More specifically, for the parallel part, the stiffness matrix of the parallel part can be obtained according to hooke's law, deformation superposition principle and parallel mechanism speed mapping relation as follows:
C L ＝{∑[S wa,i (S wa,i T C i S wa,i ) -1 S wa,i T ]+∑[S wc,i (S wc,i T C i S wc,i ) -1 S wc,i T ]} -1 (3)
wherein C is L C is a compliance matrix of the parallel portion to the end reference point i Is the flexibility matrix of the ith branched chain of the parallel part in the instantaneous coordinate system, S wa,i ，S wc,i Respectively the driving force rotation and the constraint force rotation in the ith branched force rotation space.
More specifically, the compliance of the branches i can be understood as a series superposition of the compliance of different elastomers
C i ＝C i,1 +C i,2 +…+C i,n (4)
Wherein C is i,n Representing the compliance matrix of the ith branched nth elastomer in the instantaneous coordinate system.
C i,n ＝TC n T T (5)
Wherein T is a soft transformation matrix relative to the instantaneous coordinate system, R is a rotation matrix of the instantaneous coordinate system relative to the component coordinate system, [ R ] p ×]C is an oblique matrix from the origin of the component to the end reference point n Is a compliance matrix of the component itself.
The flexibility matrix of each component can be obtained by an analytic method, a finite element method or a rigidity quality meta-model in the step K of the method.
Specifically, step E builds a performance index model of the mechanism, where the performance index model includes, but is not limited to, a dynamics model, a transmissibility model, and the like.
Specifically, step F is based on the working space, and the size parameter range of each component in the mechanism is determined, specifically as follows:
firstly, repeatedly modifying the sizes of all components and observing the working space at the tail end of a mechanism according to the established kinematic model and working space model;
then, the dimensional parameter ranges of the respective members are preliminarily determined.
And the scale parameters can be changed and the limit operation space is determined by a mechanism model drawn by three-dimensional modeling software such as SolidWorks, UG.
Specifically, step G determines the section parameter ranges of each component in the mechanism based on the quality requirement and the model of the standard component in the performance index, and specifically comprises the following steps:
firstly, determining the quality requirement of the whole machine of the robot;
then, referring to the model of each standard;
finally, a range of cross-sectional parameters for each component is determined.
Specifically, the mechanism stress analysis is performed in the step H, and the components needing topology optimization are determined as follows:
firstly, determining the whole flow method of a performance design method for synchronously optimizing the scale parameters and the topological structure of the robot, as shown in fig. 2;
and then, carrying out mechanism stress analysis through a force rotation space of the robot, and dividing all components into two groups which only need scale optimization components and need topology optimization components, wherein only the scale optimization components do not need topology optimization.
Finally, parameterized modeling is performed on components which do not need topological optimization by using Hooke's law in material mechanics.
Specifically, the step I performs topology optimization on the determined component, specifically as follows:
firstly, discretizing the scale parameters of a part needing topology optimization;
then, carrying out orthogonal experimental design by taking discrete parameters as factors, and endowing each group with equal interval mass retention ratios so as to generate parts with different specifications;
finally, each component is topologically optimized by means of ANSYS Workbench or other FEA software, and the topologically optimized load application conditions are derived from the force spin.
More specifically, the dimensional parameters of the shape rule component that need to be discretized include the length l c Radius of bottom surface r c Width w c Height h c And wall thickness t c The mass retention ratio of the topology optimization area is denoted as r, and all the common design variables can be uniformly denoted as a variable group v= [ l ] c ,w c ,h c ,r c ,t c ,r]。
Specifically, the topology optimization of the components is performed by adopting a SIMP method, and the specific process is as follows:
first, in the topology optimization process, the single finite element elastic modulus Y e By means of boundary values of 0,1]Density parameter x of (2) e Obtaining:
wherein Y is 0 The stiffness value of the material is indicated,represents a penalty factor for eliminating intermediate density values or gray elements and is typically set to p=3, y min Is a small stiffness value assigned to the void area to avoid singular effects of the design space. The lower limit of the density design variable is slightly greater than zero and is 1.0X10 -9 。
Then, as the performance design target of the robot is high rigidity and light weight, the topology optimization target of all the components is set to be the minimum flexibility; the optimization process can be expressed as:
in the method, in the process of the invention,for part compliance, U is the displacement vector，x min Is the minimum relative density, and is provided with x min =0.01. r represents the volume fraction (mass retention ratio). F is the external load vector and K is the global stiffness matrix. V is the initial design space volume, V (x e ) The final material volume is represented and correlated to the design variables in the experiment.
Finally, the topology optimization is solved using standard optimization criteria algorithms.
Optimization of iterative loop execution, convergence criteria and design variables for each finite element (i.e., density parameter x e ) The updated values are closely related. In the topology optimization execution process, differences between previous values and updated values of all unit density parameters represent the convergence degree of optimization, and when the maximum value of all the differences is not more than 0.1%, the iteration loop is ended.
Specifically, the topology structure processibility processing is performed in the step J, and the specific process is as follows:
firstly, establishing a standardized processing algorithm which enables a topological structure to meet manufacturing manufacturability;
then, a topology conforming to manufacturing manufacturability is normalized using a workability processing algorithm based on edge detection.
More specifically
Firstly, extracting the shape of the part after topological optimization by adopting an edge detection method to prepare for subsequent processing;
binarizing the segmented planar image data of each component, the gradient magnitude of each image pixel can be expressed as:
where x and y represent coordinate values of each pixel. g x (x, y) and g y (x, y) represent the gradient magnitudes along the x-axis and the y-axis, respectively, which can be obtained by the Sobel operator or other operators.
Then, note all coordinate sets of edge pixels as:
in the method, in the process of the invention,a threshold value representing the magnitude of the edge gradient;
the proposed processing algorithm is then as follows:
the first step, searching from two middle points to two ends of a processing object at the same time, and fitting a linear equation of the searching points by using a least square method until all pixel coordinates conforming to the linear characteristics are obtained;
and secondly, determining the upper and lower boundary coordinates of the line segment.
And thirdly, taking the boundary coordinates of adjacent line segments as tangent points, and inserting an inscribed arc tangent to two adjacent linear equations. If the radius of the circular arc is larger than the radius of the cutter, ending the algorithm; and otherwise, correcting the radius of the inscribed arc, updating the radius of the cutter to the radius of the arc, and analyzing the coordinates of the center of the arc and the tangent point after correction.
Specifically, the stiffness-mass meta-model is built in the step K, and the specific process is as follows:
firstly, extracting and recording compliance matrixes of components with different specifications by using software ANSYS Workbench;
the mapping of the compliance value of each component to the variable set v can then be expressed as:
diag[C g ]＝[f 1 (v) … f 6 (v)] (11)
wherein C is g Is the compliance matrix of the g-th component, f 1 (v) And f 6 (v) Representing the functions corresponding to the first and sixth major diagonal elements, respectively.
In view of the non-linearity of the mapping relationship in the above equation, the RSM is used to establish an approximate mapping between each major diagonal element of the compliance matrix and the design variable.
Specifically, taking the fourth-order function of RSM as an example, it can be expressed as:
in the formula, v i And v j Is the ith and j design variable in v. a, a 0 、b i 、c i 、d ij 、e i And f i Regression coefficient obtained by least square method, v i v j Representing the interaction of the two design variables,and->Respectively represent second, third and fourth order nonlinearities in the RSM.
Then, the parameter set outside the participatory fitting formula (12) is selected to carry out the fitting precision of the RSM. Without loss of generality, a relative Average absolute error (Average), a relative Maximum absolute error (Maximum), a Root Mean Square Error (RMSE), and an R-party (R 2 ) The error between the accuracy evaluation index calculation result and the RSM model can be expressed as:
wherein y is g An actual value representing the compliance of the component in a certain direction in group g experiments,and->Respectively y g Sum of predictive values of (2)The average value, k, is the number of parameters in the parameter set.
Finally, considering the global precision and the maximum error of the four evaluation indexes, an RSM model with high precision can be obtained.
Specifically, the step L is performed with optimal design to generate a topological structure, and the optimal scale parameters and the topological structure of the mechanism are obtained, and the specific process is as follows:
firstly, embedding the obtained rigidity-quality meta-model of each part needing topological optimization into a rigidity model and a quality model of the whole robot;
then, taking the expected rigidity as constraint, establishing a multi-objective optimization model, and optimizing by using optimization algorithms such as a PSO algorithm, a genetic algorithm and the like to obtain a Pareto front;
then, adopting a cooperative equalization criterion to select a final result, wherein the specific process is as follows:
first, the Pareto front is dimensionless processed:
wherein p 'is' n,m Represents the mth performance index value in the nth Pareto point on the Pareto boundary,and->P is respectively n,m Mean and standard deviation of (c).
Then, an optimal (minimum or maximum) value of each object is found on the Pareto boundary, and the intersection point of each optimal value is defined as an ideal point, so that the distance from the nth Pareto point to the ideal point can be expressed as:
wherein p is n,m,exc Is the optimal value of the mth performance index in the nth Pareto point, and the cooperative equilibrium point is determined to haveWith minimum D n Pareto leading edge point of (c). Taking two competing performance indicators M and S as an example, the collaborative balancing criteria are shown in fig. 3.
And finally, selecting an optimal solution to complete the integrated design of the scale parameters and the topological structure of the robot.
Example 1
Casting is one of the important means of critical component manufacturing, accounting for over 40%, and large castings are important supports for numerous core components. The cast part must have a large number of residual features such as mold closing lines, casting heads and the like, and the efficient removal of the residual features is a great difficulty facing the casting field. In the embodiment, a three-degree-of-freedom casting part residual characteristic processing robot is used as an integrated design object of scale parameters and topological structure parameters.
The mechanism consists of a plane 5R parallel mechanism and a vertical lifting device, belongs to a series-parallel mechanism easy to solve, and a kinematic model of the mechanism can be obtained by a geometric method. The 5R mechanism is schematically shown in the diagram and the coordinate system is depicted in FIG. 4.
And B, establishing a mechanism kinematics inverse solution model. Wherein the inverse kinematics of the vertical lift can be obtained directly from the Z-coordinate of the end point. The inverse kinematics of the 5R mechanism are as follows:
where each parameter definition refers to fig. 4, bc=dc=l 2 ,AB＝ED＝l1,OE＝e。
The rotational joints are limited as follows: θ 1 And theta 2 And the angle CDE and the angle CBA are between 65 degrees and 170 degrees and are larger than 20 degrees.
The working space of the mechanism can be obtained by searching x and y coordinates by adopting a limit searching method with the step length of 1 mm.
Step C, based on the kinematic model, the driving force of the mechanism is obtained as follows
The constraint spin to obtain the branch ABC is as follows:
the force spin space of the branched chain ABC is:
S w,1 ＝[S wa,1 S wc1,1 S wc2,1 S wc3,1 ]
the force rotation of the branched chain DE is similar to the above formula.
The rigidity model of the mechanism is formed by connecting a 5R mechanism and a vertical lifting device in series:
K＝(C 5R +C P ) -1
wherein C is 5R ，C P Compliance of 5R mechanism and vertical lift, C P Is obtained by direct extraction of finite element software, C 5R Obtained by the formula:
C 5R ＝(S w,i (S w,i T C i S w,i ) -1 S w,i T ) -1 ,i＝1,2
wherein C is i From l 1 ，l 2 The flexibility of the two connecting rods is directly overlapped.
And D, according to engineering requirements of casting piece residual feature processing, the xy working space of the obtained robot is larger than 1.2m multiplied by 0.5m, and the z-direction rigidity is larger than 1N/mu m. The optimization index is the maximum rigidity and the minimum mass, and other performance indexes are not needed.
Step E. Because the 5R mechanism is simpler, isThe workload is reduced, the key rod length can be directly determined according to the working space constraint and the common proportion, l 1 ＝0.725m，l 2 ＝0.956m。
The part of the F.5R mechanism requiring structural optimization is a near-frame rod l 1 And a far hack lever l 2 The key cross-sectional parameters include width, height and thickness. According to weight constraint, the optimization ranges are respectively as follows: general hack lever [220mm,260mm]、[185mm,215mm]And [16mm,20mm]The method comprises the steps of carrying out a first treatment on the surface of the The far hack lever [190mm,230mm]、[145mm,175mm]、[12mm,16mm]。
G, designing three-factor three-level orthogonal tests, wherein each near rack rod or far rack rod is provided with 9 experimental groups; to investigate the relationship between mass, topology and stiffness, 5 equally spaced mass retention ratios r1 and r2, each ranging from [55%,83% ], were set for each set of experiments.
Thus, there were 4 topology optimization variables, and eventually 45 experimental groups per proximal or distal rack. Thereafter, 90 experimental groups were topologically optimized using the "Static Analysis" and "Topology Optimization" modules in ANSYS, and a "Program Controlled" solver was selected for solving. The acting force and the fixed point are respectively arranged at two ends of the connecting rod, and the acting force is vertically downward in the z direction.
And H, after all topological optimization results of the near hack lever and the far hack lever are obtained, carrying out the following treatment on the near hack lever and the far hack lever by utilizing a machinability treatment algorithm:
a. dividing the design domain after topological optimization into four faces according to the connecting rod composition;
b. adopting a machinability processing algorithm to process different surfaces;
c. and removing the corresponding part of the three-dimensional model of the part according to the obtained geometric characteristics.
The workability treatment is shown in fig. 5, for example.
Step I, extracting and recording compliance matrixes of components with different specifications by using software ANSYS Workbench to obtain a rigidity quality element model of the near frame rod and the side link rod:
wherein, the near hack lever
zk lx ＝-2.4×10 9 +1.6×10 7 w 1 +2.2×10 7 h 1 -6.8×10 7 r 1
-3.1×10 7 t 1 -3.2×10 4 w 1 2 -4.9×10 4 h 1 2 +9.4×10 5 r 1 2 +9.3×10 5 t 1 2
-9.1×10 3 w 1 h 1 +6.6×10 3 w 1 r 1 +6.9×10 3 h 1 r 1 +3.2×10 4 r 1 t 1 -4.3×10 3 r 1 3
zk ly ＝-4.4×10 10 +2.6×10 8 w 1 +2.6×10 8 h 1 -5.1×10 8 r 1
-1.6×10 8 t 1 -4.8×10 5 w 1 2 -4.9×10 5 h 1 2 +7.4×10 6 r 1 2 +9.6×10 6 t 1 2
-2.5×10 5 w 1 h 1 +2.6×10 5 w 1 r 1 -9.7×10 4 h 1 r 1 -1.6×10 6 r 1 t 1 -3.4×10 4 r 1 3
zk lz ＝-8.1×10 9 +5.2×10 7 w 1 -1×10 7 h 1 -3.9×10 6 r 1
+3.4×10 8 t 1 -8.7×10 4 w 1 2 +5.6×10 4 h 1 2 +4.2×10 4 r 1 2
-9.2×10 6 t 1 2 -5.5×10 4 w 1 h 1 +2.3×10 4 w 1 r 1 +1.7×10 4 h 1 r 1 -2.9×10 5 r 1 t 1
zk ax ＝-1.37×10 9 +7.4×10 6 w 1 -6.6×10 5 h 1 +2.1×10 6 r 1
+4.8×10 7 t 1 -1.2×10 4 w 1 2 +6.3×10 3 h 1 2 +7.6×10 3 r 1 2
-1.2×10 6 t 1 2 -6.0×10 3 w 1 h 1 -2.4×10 3 w 1 r 1 -3.8×10 3 h 1 r 1 -4.5×10 4 r 1 t 1
zk ay ＝-2.3×10 8 +1.4×10 6 w 1 +6.2×10 5 h 1 -9.8×10 5 r 1
+2.9×10 6 t 1 -3.0×10 3 w 1 2 -1.6×10 3 h 1 2 +6.1×10 3 r 1 2
-7.9×10 4 t 1 2 +1.8×10 2 w 1 h 1 +1.0×10 3 w 1 r 1 +9.2×10 2 h 1 r 1 -1.0×10 3 r 1 t 1
zk az ＝-3.1×10 9 +1.1×10 7 d 1 +1.9×10 7 h 1 -1.2×10 7 r 1
+1.7×10 7 t 1 -2.0×10 4 d 1 2 -4.2×10 4 h 1 2 +1.6×10 5 r 1 2 -4.9×10 5 t 1 2
-9.8×10 3 d 1 h 1 +1.2×10 3 d 1 r 1 +3.4×10 3 h 1 r 1 -3.8×10 3 r 1 t 1 -7.7×10 2 r 1 3
Wherein, the side link
ck lx ＝-4.0×10 8 +6.2×10 6 w 2 -3.9×10 6 h 2 +2.4×10 6 r 2
-1.3×10 7 t 2 -1.8×10 4 w 2 2 +4.9×10 3 h 2 2 -2.1×10 4 r 2 2 +5.8×10 5 t 2 2
+8.9×10 3 w 2 h 2 +3.9×10 2 w 2 r 2 +3.4×10 3 w 2 t 2 +1.1×10 4 h 2 r 2 -1.1×10 4 r 2 t 2
ck ly ＝-1.2×10 10 +1.4×10 8 w 2 -5.×10 7 h 2 +1.1×10 8 r 2 -1.4×10 8 t 2
-3.9×10 5 w 2 2 -3.8×10 4 h 2 2 -2.2×10 6 r 2 2 +2.1×10 7 t 2 2 +1.3×10 5 w 2 r 2
+2.5×10 5 w 2 h 2 +1.8×10 5 h 2 r 2 +3.4×10 5 r 2 t 2 +1.1×10 4 r 2 3 -1.8×10 6 w 2 t 2
ck lz ＝-5.9×10 7 +1.7×10 6 w 2 +1.0×10 7 h 2 -1.0×10 7 r 2
-9.7×10 7 t 2 -2.0×10 4 w 2 2 -5.1×10 4 h 2 2 +3.4×10 6 t 2 2 +3.6×10 4 w 2 r 2
+2.4×10 4 w 2 h 2 +2.0×10 4 h 2 r 2 +1.5×10 4 r 2 2 -4.7×10 4 r 2 t 2 +5.8×10 4 w 2 t 2
ck ax ＝-1.3×10 8 +2.9×10 6 w 2 +1.7×10 6 h 2 -3.9×10 6 r 2
-3.0×10 7 t 2 -1.2×10 4 w 2 2 -1.4×10 4 h 2 2 +7.8×10 3 r 2 2 +1.2×10 6 t 2 2
+1.1×10 4 w 2 h 2 +1.1×10 4 w 2 r 2 +7.4×10 3 h 2 r 2 +6×10 3 r 2 t 2 -2×10 4 w 2 t 2
ck ay ＝2.8×10 8 +4.4×10 6 w 2 -6.2×10 5 h 2 -4.3×10 5 r 2
-2.8×10 6 t 2 -1.6×10 3 w 2 2 +7.6×10 2 h 2 2 +3.8×10 2 r 2 2 +1.2×10 5 t 2 2
+1.4×10 3 w 2 h 2 +1.1×10 3 w 2 r 2 +1.7×10 3 h 2 r 2 -1.4×10 3 r 2 t 2 -1.7×10 3 w 2 t 2
ck az ＝-2.4×10 9 +3.5×10 6 w 2 -1.5×10 6 h 2 +8.1×10 5 r 2
-7.9×10 6 t 2 -5.3×10 3 r 2 2 +5.4×10 5 t 2 2 +1.1×10 3 h 2 2 -9.5×10 3 w 2 2
+5.1×10 3 w 2 h 2 +4×10 2 w 2 r 2 +9.1×10 3 r 2 t 2 -3×10 4 w 2 t 2 +1.1×10 3 h 2 r 2
And J, solving by utilizing a PSO algorithm driven by Matlab and Isight software in a combined way based on the optimization model and the setting, wherein specific parameters of the PSO algorithm are set as follows in order to ensure the convergence and the robustness of the algorithm: global learning coefficient and Personal learning coefficient are 1.49,Maximum iterations and Number of particles are 50,Initial weight are 0.729.
The total number of feasible solutions obtained by optimization is 2516, and 386 feasible solutions meeting each constraint condition are provided, wherein 104 feasible solutions form a Pareto front. The initial topology and the final topology are shown in fig. 6.
The method establishes algebraic relation of the topological structure, the scale and the performance of the mechanism, comprehensively considers the coupling influence rule of the topological structure and the scale on the performance, solves the problem of mutual fracture of topological structure design and scale design, and has excellent optimizing capability.
Claims (10)
1. A design method for integrating robot scale parameters and topological structures is characterized in that: the method comprises the following steps:
A. determining a mechanism type of the robot, and selecting a mathematical tool according to the mechanism type;
B. establishing a kinematic model and a working space model of a mechanism;
C. establishing a rigidity model of the mechanism;
D. according to the application scene of the robot, determining working space, rigidity and performance indexes which need to be met by the robot;
E. establishing a performance index model of the mechanism;
F. determining a size parameter range of each component in the mechanism based on the working space;
G. determining the section parameter range of each component in the mechanism based on the quality requirement in the performance index and the model of the standard component;
H. carrying out mechanism stress analysis to determine a component needing topology optimization;
I. performing topology optimization on the determined components;
J. carrying out topology structure processing;
K. establishing a rigidity-quality meta-model;
and L, carrying out optimal design to generate a topological structure, and obtaining the optimal scale parameters and the topological structure of the mechanism.
2. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 1, wherein the method comprises the following steps: step A, determining the mechanism type of the robot, and selecting a mathematical tool according to the mechanism type, wherein the specific process is as follows:
firstly, judging whether a closed loop branched chain exists in a mechanism;
then judging whether a serial structure exists in the mechanism or not;
then, determining whether the mechanism is a serial mechanism, a parallel mechanism or a series-parallel mechanism;
finally, a corresponding mathematical tool is selected according to the type of the mechanism.
3. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 1, wherein the method comprises the following steps: and B, establishing a kinematic model and a working space model of the mechanism, wherein the specific process is as follows:
firstly, solving a kinematic forward and inverse solution of a mechanism based on the obtained mechanism type and a selected mathematical tool;
and then, establishing and obtaining the working space constraint of the mechanism according to the obtained forward and reverse solutions.
4. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 1, wherein the method comprises the following steps: and C, establishing a rigidity model of the mechanism, wherein the specific process is as follows:
firstly, obtaining a kinematic model based on the step B, and establishing a force rotation space and a motion rotation space of a mechanism;
and then obtaining the rigidity connection relation of each module of the mechanism according to the serial-parallel characteristics of the mechanism.
5. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 1, wherein the method comprises the following steps: step D, according to the application scene of the robot, determining the working space, rigidity and performance indexes which the robot needs to meet, wherein the specific process is as follows:
firstly, determining an application scene of a robot to obtain application scene requirements;
and then, according to the specific application scene requirements, determining the working space, the rigidity requirement and the performance index of the tail end of the mechanism.
6. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 1, wherein the method comprises the following steps: and step I, performing topology optimization on the determined components, wherein the specific process is as follows:
firstly, combining scale parameters by using an orthogonal experiment method;
then, according to the combination result, obtaining components with different specifications under different combination conditions;
and then, carrying out topological optimization on the component to be optimized by utilizing finite element software.
7. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 1, wherein the method comprises the following steps: and (C) carrying out topology structure processability treatment, wherein the specific process is as follows:
firstly, establishing a standardized processing algorithm which enables a topological structure to meet manufacturing manufacturability;
then, a topology conforming to manufacturing manufacturability is normalized using a workability processing algorithm based on edge detection.
8. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 1, wherein the method comprises the following steps: and (K) establishing a rigidity-quality meta-model, wherein the specific process is as follows:
firstly, extracting the rigidity of each component by means of FEA software;
then, constructing the mapping of each component scale parameter and the rigidity and the quality of each component scale parameter by using RSM;
finally, a stiffness-mass meta-model of the topology optimization component is formed.
9. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 1, wherein the method comprises the following steps: and step L, carrying out optimal design to generate a topological structure, and obtaining optimal scale parameters and the topological structure of the mechanism, wherein the specific process is as follows:
firstly, embedding all obtained component rigidity-mass element models into a robot complete machine rigidity model and a mass model;
then, solving by adopting an optimization algorithm to obtain a Pareto front by using the determined optimization target;
and finally, selecting an optimal result from the Pareto front according to the cooperative balance point criterion, thereby obtaining the optimal scale parameter and the topological structure of the mechanism.
10. The method for designing the integration of the dimension parameters and the topological structure of the robot according to claim 9, wherein the method comprises the following steps: the specific target of the determined optimization target is as follows:
and D, taking the maximum rigidity as a target, the minimum mass as a target and taking the performance index determined in the step D as an optimization target.
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