CN117610381B - Robot structure lightweight design method based on assembly finite element analysis - Google Patents
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Abstract
The invention provides a robot structure lightweight design method based on assembly finite element analysis, which comprises the following steps: establishing a finite element model of the robot assembly body, and setting boundary conditions according to the actual working conditions of the robot; finite element analysis is carried out on the part to be optimized, and the corresponding robot gesture when the part to be optimized is in a limit working condition is obtained; determining an optimization area of a part to be optimized; and performing topological optimization on an optimized region of the part to be optimized according to the corresponding robot gesture when the robot is in the limit working condition. According to the invention, the errors of analysis results and actual conditions caused by equivalent constraint and load can be avoided by establishing the finite element model of the robot assembly; selecting various typical working conditions to perform finite element analysis on the sample, so that an analysis result is more representative; and determining the limit stress distribution condition of each part according to the analysis result, ensuring that corresponding constraint conditions and boundary conditions are consistent with the actual conditions during topological optimization, and realizing the effective lightweight design of the robot.
Description
Technical Field
The invention relates to the technical field of deep learning, in particular to a robot structure lightweight design method based on assembly finite element analysis.
Background
Currently, the working scene of robots is gradually expanding from a structured, known industrial environment to unstructured, unknown scenes of medical, service, etc. Under such a scene, the robot is in direct contact with the human body, the safety is important to consider in the design, and the damage caused by collision with the human body when the robot is out of control can be reduced due to the lighter body mass. Therefore, the light weight is a key of the research of the man-machine cooperation type robot. The existing light-weight method is mainly developed from two aspects of material selection and structural design, and the light-weight method based on the material is mainly realized by selecting a novel material which has both performance and light weight, but the material is often high in price and difficult to process. Therefore, designers are more inclined to achieve a lightweight design of the robot body through structural optimization. The structural optimization method based on topological optimization is a reasonable and effective robot structure lightweight design method, the reasonable distribution of part materials in actual working conditions is determined through an algorithm, the existence of redundant materials can be effectively avoided, and the structural optimization method has remarkable advantages compared with the traditional structural optimization method for realizing weight reduction on modification of the size and the shape of the existing structure.
However, when the existing topology optimization method for robot weight reduction is used for building a topology optimization finite element model, the topology optimization finite element model is usually built based on a single part, constraint and load of the part are equivalent values set according to the assembly condition of the part in a robot assembly body, and stress distribution and strain inside the part deviate from actual conditions according to the Saint-Venant' S PRINCIPLE under the equivalent constraint and equivalent load conditions, so that the final topology optimization result is affected.
Disclosure of Invention
To achieve the above and other advantages and in accordance with the purpose of the present invention, a robot structure lightweight design method based on assembly finite element analysis includes the steps of:
Establishing a finite element model of the robot assembly body, and setting boundary conditions according to the actual working conditions of the robot;
Performing finite element analysis on a part to be optimized in the finite element model of the robot assembly to obtain a corresponding robot gesture when the part to be optimized is in a limit working condition;
determining an optimization area of the part to be optimized;
and performing topological optimization on the optimized region of the part to be optimized through the corresponding robot gesture when the robot is in the limit working condition.
Further, the building of the robot assembly finite element model comprises the following steps:
simplifying a robot model;
Importing the simplified robot model into finite element simulation analysis software;
adding materials for design to all parts;
performing grid division on the robot model;
and (3) increasing the network density of the parts with the structural feature complexity reaching the threshold value, and completing the establishment of the finite element model of the robot assembly.
Further, the finite element analysis of the part to be optimized in the robot assembly finite element model comprises the following steps:
dividing the structure body into a plurality of units, wherein the units are connected through nodes;
respectively solving the rigidity matrixes of all the units, integrating the rigidity matrixes into an overall rigidity matrix, and forming an overall balance equation, wherein the formula is as follows:
,
wherein, For the total stress,/>Is an overall stiffness matrix,/>Is the whole node displacement vector;
introducing boundary conditions, calculating the displacement of each unit node, and calculating the stress and the strain of each unit according to the displacement of each unit node, wherein the formula is as follows:
,
wherein, For any point displacement within a cell,/>Is a unit geometric matrix,/>Is any point stress in the unit,/>Is an elastic matrix,/>Is a unit node displacement matrix.
Further, the finite element analysis of the part to be optimized in the robot assembly finite element model comprises the following steps:
determining the relevant posture of the robot under the actual working condition;
Taking the representative position of the joint in each group of actions of the robot as a typical working condition, and carrying out finite element analysis to obtain a representative part stress distribution condition;
and obtaining the corresponding robot gesture when the part to be optimized has the maximum stress through comparative analysis.
Further, the non-optimized region of the part to be optimized includes the junction.
Further, the topology optimization of the optimized region of the part to be optimized by the corresponding robot gesture when the robot is in the limit working condition comprises the following steps:
taking the overall balance equation as a boundary condition of topology optimization;
determining design variables through a topology optimization algorithm;
And performing topological optimization on the part to be optimized based on the corresponding robot gesture setting target and constraint when the part to be optimized is in the limit working condition.
Further, the determining of the design variable through the topology optimization algorithm comprises the step of taking the relative density of the units as the design variable through a topology optimization method based on a variable density method; the mathematical model of the variable density method is as follows:
,
wherein, Representing the relative density of the ith grid,/>N is the grid number, M represents the total mass of the structure, for the design variables,/>Representing the volume of the ith grid,/>As constraint function,/>For constraint condition,/>Is the minimum relative density,/>Representing an N-dimensional real set.
Further, the topological optimization of the part to be optimized based on the corresponding robot gesture setting target and constraint when the part to be optimized is in the limit working condition comprises taking the minimum mass as an optimization target and taking the deformation of the tail end of the robot as a constraint condition.
Further, the proportional relation of the terminal deformation constraint values of different length models:
,
wherein, The deformation of the tail end of the cantilever beam is represented by F, the tail end load is represented by l, the length of the cantilever beam is represented by E, the elastic modulus is represented by I, and the moment of inertia is represented by I; /(I)L is the optimized model length and the reference mechanical arm length,/>, respectivelyIs the corresponding maximum amount of terminal deformation.
Further, the part to be optimized of the robot is determined according to the use condition and the quality of the part and the shape characteristics;
The finite element analysis of the part to be optimized in the finite element model of the robot assembly further comprises the following steps: and adding the displayed analysis results according to the requirements.
Compared with the prior art, the invention has the beneficial effects that:
The invention provides a robot structure lightweight design method based on assembly finite element analysis, which can avoid errors of analysis results and actual conditions caused by equivalent constraint and load by establishing a robot assembly finite element model. In addition, the motion gesture of the exoskeleton robot is analyzed, and various typical working conditions are selected to conduct finite element analysis on the exoskeleton robot, so that an analysis result is more representative. And then determining the limit stress distribution condition of each part according to the analysis result, thereby ensuring that corresponding constraint conditions and boundary conditions are consistent with the actual conditions in the topological optimization, realizing the weight reduction to the greatest extent on the basis of ensuring that the usability of the part meets the requirements of the actual working conditions, and further realizing the effective lightweight design of the robot.
The foregoing description is only an overview of the present invention, and is intended to provide a better understanding of the present invention, as it is embodied in the following description, with reference to the preferred embodiments of the present invention and the accompanying drawings. Specific embodiments of the present invention are given in detail by the following examples and the accompanying drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a flowchart of a robot structure lightweight design method based on assembly finite element analysis of embodiment 1;
FIG. 2 is a flow chart II of a lightweight design method for a robot structure based on assembly finite element analysis in accordance with embodiment 1;
FIG. 3 is a flow chart of the finite element model of the robot assembly of example 1;
FIG. 4 is a flow chart of finite element analysis of a part to be optimized in a finite element model of a robot assembly according to example 1;
FIG. 5 is a flow chart II of finite element analysis of a part to be optimized in a finite element model of a robot assembly according to embodiment 1;
FIG. 6 is a flow chart of topology optimization of an optimized region of a part to be optimized according to the robot pose corresponding to the robot in the limit condition in embodiment 1;
FIG. 7 is a schematic diagram showing the comparison of the displacement of the part nodes under the condition of equivalent constraint and actual constraint;
Fig. 8 is a schematic diagram of a storage medium of embodiment 2.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and detailed description, wherein it is to be understood that, on the premise of no conflict, the following embodiments or technical features may be arbitrarily combined to form new embodiments.
Example 1
When the structural topology optimization is carried out by utilizing the integral model method, the integral finite element model of the robot is required to be established and subjected to finite element analysis, and then the part structure is optimized by combining a specific topology optimization algorithm based on the analysis result. As shown in fig. 1 and 2, the method comprises the following steps:
S1, establishing a finite element model of a robot assembly body, and setting boundary conditions including external load and constraint according to the actual working condition of the robot;
wherein, as shown in fig. 3, the robot assembly finite element model is established by the following steps:
S11, simplifying a robot model in consideration of complex features of an initial model of the robot; for example, parts with less influence on the calculation result, such as functional parts, non-bearing parts and the like, are omitted; the characteristics of chamfer angle, boss, concave part, flanging, welding line of the welding piece and the like are ignored as much as possible; some threaded holes that have less impact on the analysis results should be removed, etc.
S12, importing the simplified robot model into finite element simulation analysis software;
s13, adding materials for designing all parts;
s14, carrying out grid division on the robot model;
S15, in order to improve accuracy of analysis results, network density of parts with structural feature complexity reaching a threshold value is increased, and establishment of a finite element model of the robot assembly body is completed.
S2, carrying out finite element analysis on the part to be optimized in the finite element model of the robot assembly to obtain a corresponding robot gesture when the part to be optimized is in a limit working condition, and adding a displayed analysis result according to requirements, wherein the analysis result comprises stress, strain, deformation and the like; as shown in fig. 4, the method specifically comprises the following steps:
S21, firstly dividing the structure body into a plurality of units, and connecting the units through nodes;
S22, respectively obtaining the rigidity matrix of each unit Integrated into an overall stiffness matrix K and forming an overall balance equation formula:
（1）,
wherein F is total stress, K is total rigidity matrix, Is the whole node displacement vector;
S23, introducing a displacement boundary condition on the basis, obtaining the displacement of each unit node, and finally obtaining the stress and the strain of each unit through the displacement of each unit node, wherein the formula is as follows:
（2），
wherein, For any point displacement in a unit, B is a unit geometric matrix,/>Is the stress at any point in the unit, D is an elastic matrix,/>Is a unit node displacement matrix.
Because the existing topology optimization method is used for designing the related parts of the robot in a light-weight manner, stress analysis is usually carried out by only considering a limit gesture and a motion loading condition of the robot, and then an optimized object topology structure is solved according to an analysis result (simplex Kuang Tapu optimization). However, as the pose of the robot changes with time during operation, the stress distribution of the component parts changes with the change, and the lightweight design of the parts is only carried out based on one pose of the robot, so that the representativeness is lacking, and the optimization effect of the obtained parts cannot be ensured. Therefore, the method comprehensively considers various working conditions of the working movement of the robot, and has important engineering significance for topological optimization of the parts.
In this embodiment, when finite element analysis is performed on a part to be optimized in a finite element model of a robot assembly, an actual limit condition of a robot needs to be determined first.
For a multi-degree-of-freedom serial robot, as the robot motion is continuous motion changing along with the joint angle, finite element analysis cannot be performed on all the postures of the robot.
Therefore, in this embodiment, as shown in fig. 5, the steps of:
S200, firstly, determining the relevant gesture of the robot under the actual work;
s210, carrying out finite element analysis by taking the representative position of the joint in each group of actions of the robot as a typical working condition to obtain a representative part stress distribution condition;
S220, obtaining the corresponding robot gesture when the part to be optimized has the maximum stress through comparative analysis.
According to the method, according to the movement range of each joint of the robot, the initial position, the final position and the middle position of the joint in the range are taken, the corresponding robot pose can be obtained based on the corresponding combination of the joint positions, finite element analysis is carried out on the parts to be optimized based on the pose, the corresponding robot pose when the parts to be optimized are in the limiting working condition can be obtained by analyzing the stress conditions of the parts under different poses, optimization of the parts can be carried out based on the pose, and excessive material removal is ensured when the parts are subjected to structural topological optimization, so that the performance of the optimized parts cannot meet specific use.
FIG. 7 is a schematic diagram showing the comparison of the displacement of the part nodes under the condition of equivalent constraint and actual constraint. FIG. 7 (a) certain cell node displacements when an equivalent constraint boundary is added to the part boundary; fig. 7 (b) shows some cell node displacements when the part boundaries are actual constraints.
The displacement boundary conditions are the limits of certain unit nodes in terms of positions and directions, and can be divided into two types, wherein one type is that the displacement of the node n along a certain direction is zero, equivalent fixed end constraint is set for a part to be optimized, and the other type is that the displacement of the node n along a certain direction is a given value, and the displacement corresponds to the constraint of the part in an assembly body. When the displacement boundary conditions are different, the obtained node displacement is also different, so that the internal stress and strain analysis result of the part is deviated from the actual state, the topological optimization result of the part is guided to the wrong direction, and finally the light weight effect is influenced. In this embodiment, the limit condition selection and the finite element model establishment during the topology optimization of the robot include the determination of the boundary condition. Therefore, the method ensures the accuracy of finite element model establishment and the limit working condition determination of the robot during optimization, and has important significance for improving the effect of topological optimization in the light weight of the robot.
S3, determining an optimized area of the part to be optimized after determining the pose of the robot corresponding to the limit working condition of the part to be optimized; the selection principle is that the non-optimized areas of the parts to be optimized mainly select the connection parts, including holes, keys, grooves and the like, so as to ensure the assembly of the optimized parts.
S4, performing topological optimization on an optimized region of the part to be optimized through the corresponding robot gesture when the robot is in the limit working condition. As shown in fig. 6, the method specifically comprises the following steps:
S41, realizing topological optimization of the parts based on finite element analysis results, and taking an overall balance equation (namely formula (1)) as a boundary condition of topological optimization;
S42, determining design variables through a topology optimization algorithm; specifically, a topological optimization method based on a variable density method (SIMP) takes the relative density of units as a design variable; the mathematical model of the variable density method is as follows:
（3）,
wherein, Representing the relative density of the ith grid,/>N is the grid number, M represents the total mass of the structure, for the design variables,/>Representing the volume of the ith grid,/>As a constraint function (which may be a displacement, mass, stress, etc. constraint),Optimizing constraints in a mathematical model for a structural topology,/>Is the minimum relative density,/>Representing an N-dimensional real set.
S43, performing topological optimization on the part to be optimized based on the corresponding robot gesture setting target and constraint when the part to be optimized is in the limit working condition.
The rigidity of the part is influenced by the structural change of the part, so that the deformation of the tail ends of the multi-degree-of-freedom serial robots under rated load is changed, and the working accuracy of the robots is influenced by the larger deformation of the tail ends. Therefore, the embodiment takes the minimum mass as an optimization target and the deformation of the tail end of the robot as a constraint condition.
The embodiment determines the deformation based on actually measuring the maximum end deformation of the commercial man-machine cooperative arm under the rated load condition.
According to a calculation formula of the end deformation of the cantilever beam in the material mechanics:
（4）,
wherein, The deformation of the tail end of the cantilever beam is represented by F, the tail end load is represented by l, the length of the cantilever beam is represented by E, the elastic modulus is represented by E, and the moment of inertia is represented by I.
From this, the proportional relation of the end deformation constraint values of the different length models can be deduced:
（5）
wherein, L is the optimized model length and the reference mechanical arm length,/>, respectivelyIs the corresponding maximum amount of terminal deformation.
Therefore, based on the formula (5), the end variable constraint corresponding to the topological optimization of the serial robots under different working conditions can be obtained.
And then judging whether convergence is carried out, if so, outputting an optimization result, otherwise, returning to the step S2 to continue execution.
The present embodiment is exemplified by a 5-degree-of-freedom upper limb rehabilitation training robot structure lightweight design.
And determining the part to be optimized of the robot according to the specific use working condition and the quality of the part and shape characteristics, and realizing the lightweight design of the robot through the structural optimization of the part to be optimized. When the method provided by the invention is adopted to optimize the part, finite element analysis is firstly required to be carried out on the part to be optimized, and a robot assembly finite element model is established for avoiding the equivalent constraint added by independent analysis and the deviation between the load and the actual load. Firstly, simplifying a robot model, removing part features such as fillets, threaded holes and chamfers which do not affect the accuracy of analysis results, introducing the simplified model into finite element simulation analysis software, adding materials for design for all parts, and then meshing the model. In order to improve the accuracy of analysis results, the grid density of parts with complex structural features is increased, the finite element model establishment of the assembly is finally completed, and then the boundary conditions are set according to the actual working conditions of the robot.
After the finite element model is built, finite element analysis can be performed, as the upper limb rehabilitation robot has the function of assisting the complete upper limb rehabilitation training robot of a patient, the working space of the robot needs to meet the requirement of the degree of freedom of the movement of the upper limb of the human body, the postures of the robot under different upper limb actions are greatly different, and the postures of the robot corresponding to the limiting working conditions of different parts to be optimized selected in the robot are also possibly different. Therefore, for each part to be optimized, firstly, the corresponding robot gesture when the part to be optimized is in a limiting working condition is required to be determined, namely, for 5 joints of the robot, the initial, middle and end angles in the motion range of each joint are taken, the 5 joints are combined to represent the gesture of the robot under various working conditions, finite element analysis is carried out based on the gesture, the joint corresponding angle combination corresponding to the maximum stress of the selected part to be optimized is obtained through comparison analysis, and then topological optimization can be carried out on the part to be optimized based on the gesture of the robot.
And after the pose of the robot corresponding to the limiting working condition of the part to be optimized is determined, setting an optimization area corresponding to the part to be optimized. The selection principle is that the non-optimized area of each part mainly selects the connection, including holes, keys, grooves, etc.
Then optimizing the part to be optimized, wherein the method is a topological optimization method based on a variable density method, the selected design variable is the unit relative density, the part to be optimized is optimized based on the robot gesture corresponding to the limit working condition of the part to be optimized determined in the step S2, the optimization target is set to be minimum in mass, the structural change of the part is considered to influence the rigidity of the part, the deformation of the tail end of the rated load robot is changed, the working accuracy of the robot is influenced by the larger deformation of the tail end, therefore, the rigidity of the designed part is used as a constraint condition, and the part to be optimized is optimized based on the constraint condition.
According to the invention, the part is kept in the assembly body for finite element analysis, so that the load boundary condition and the constraint condition of the part are ensured to be in accordance with the actual condition, and the boundary condition generated by the topological structure can be ensured to be in accordance with the actual project when the part topology is optimized, thereby avoiding the situation that the optimized structure cannot meet the use requirement.
Example 2
A computer readable storage medium, as shown in fig. 8, having stored thereon program instructions that when executed implement a robot structural lightweight design method based on assembly finite element analysis. For detailed description of the method, reference may be made to corresponding descriptions in the above method embodiments, and details are not repeated here.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises an element.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments.
The foregoing is illustrative of the embodiments of the present disclosure and is not to be construed as limiting the scope of the one or more embodiments of the present disclosure. Various modifications and alterations to one or more embodiments of this description will be apparent to those skilled in the art. Any modifications, equivalent substitutions, improvements, or the like, which are within the spirit and principles of one or more embodiments of the present disclosure, are intended to be included within the scope of the claims of one or more embodiments of the present disclosure.
Claims (6)
1. The robot structure lightweight design method based on the assembly finite element analysis is characterized by comprising the following steps of:
Establishing a finite element model of the robot assembly body, and setting boundary conditions according to the actual working conditions of the robot;
Performing finite element analysis on a part to be optimized in the finite element model of the robot assembly to obtain a corresponding robot gesture when the part to be optimized is in a limit working condition;
determining an optimization area of the part to be optimized;
performing topological optimization on the optimized region of the part to be optimized through the corresponding robot gesture when the robot is in the limit working condition;
the finite element analysis of the part to be optimized in the robot assembly finite element model comprises the following steps:
dividing the structure body into a plurality of units, wherein the units are connected through nodes;
respectively solving the rigidity matrixes of all the units, integrating the rigidity matrixes into an overall rigidity matrix, and forming an overall balance equation, wherein the formula is as follows:
，
wherein, For the total stress,/>Is an overall stiffness matrix,/>Is the whole node displacement vector;
introducing boundary conditions, calculating the displacement of each unit node, and calculating the stress and the strain of each unit according to the displacement of each unit node, wherein the formula is as follows:
，
wherein, For any point displacement within a cell,/>Is a unit geometric matrix,/>Is any point stress in the unit,/>Is an elastic matrix,/>A displacement matrix is used as a unit node;
the finite element analysis of the part to be optimized in the robot assembly finite element model comprises the following steps:
determining the relevant posture of the robot under the actual working condition;
Taking the representative position of the joint in each group of actions of the robot as a typical working condition, and carrying out finite element analysis to obtain a representative part stress distribution condition;
Obtaining the corresponding robot gesture when the maximum stress exists in the part to be optimized through comparative analysis;
The topology optimization of the optimized region of the part to be optimized through the corresponding robot gesture when the robot is in the limit working condition comprises the following steps:
taking the overall balance equation as a boundary condition of topology optimization;
determining design variables through a topology optimization algorithm;
Performing topological optimization on the part to be optimized based on the corresponding robot gesture setting target and constraint when the part to be optimized is in the limit working condition;
The method for determining the design variable through the topology optimization algorithm comprises the steps that a topology optimization method based on a variable density method takes unit relative density as the design variable; the mathematical model of the variable density method is as follows:
，
wherein, Representing the relative density of the ith grid,/>For design variables,/>For the number of grids,/>Representing the total mass of the structure,/>Representing the volume of the ith grid,/>As constraint function,/>For constraint condition,/>Is the minimum relative density,/>Representing an N-dimensional real set.
2. The robotic structure lightweight design method based on assembly finite element analysis of claim 1, wherein: the method for establishing the finite element model of the robot assembly body comprises the following steps of:
simplifying a robot model;
Importing the simplified robot model into finite element simulation analysis software;
adding materials for design to all parts;
performing grid division on the robot model;
and (3) increasing the network density of the parts with the structural feature complexity reaching the threshold value, and completing the establishment of the finite element model of the robot assembly.
3. The robotic structure lightweight design method based on assembly finite element analysis of claim 1, wherein: the non-optimized region of the part to be optimized includes the junction.
4. The robotic structure lightweight design method based on assembly finite element analysis of claim 1, wherein: the topological optimization of the part to be optimized based on the corresponding robot gesture setting target and constraint when the part to be optimized is in the limit working condition comprises taking the minimum mass as an optimization target and taking the deformation of the tail end of the robot as a constraint condition.
5. The robot structural lightweight design method based on the assembly finite element analysis according to claim 4, wherein: proportional relation of terminal deformation constraint values of different length models:
，
，
wherein, The deformation of the tail end of the cantilever beam is represented by F, the tail end load is represented by l, the length of the cantilever beam is represented by E, the elastic modulus is represented by I, and the moment of inertia is represented by I;、/> Respectively optimizing the length of the model and the length of the reference mechanical arm,/> 、/>Is the corresponding maximum amount of terminal deformation.
6. The robotic structure lightweight design method based on assembly finite element analysis of claim 1, wherein: the part to be optimized of the robot is determined according to the use condition and the quality of the part and the shape characteristics;
The finite element analysis of the part to be optimized in the finite element model of the robot assembly further comprises the following steps: and adding the displayed analysis results according to the requirements.
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