CN108268745A - A kind of binary tree robot milling system frequency response Forecasting Methodology based on RCSA - Google Patents
A kind of binary tree robot milling system frequency response Forecasting Methodology based on RCSA Download PDFInfo
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Abstract
The present invention relates to robotic milling manufacture field, and a kind of binary tree robot milling system frequency response Forecasting Methodology based on RCSA is disclosed, including：(a) milling system is divided into minor structure B, minor structure A and flexible junctures；(b) minor structure B frequency response functions are obtained and its modal parameter is standardized, solve modal parameters and coupling function of the minor structure B under posture to be solved；(c) minor structure A finite element models are established and optimize its cutter material parameter, obtain its frequency response function and response matrix；(d) experiment measures integrally-built frequency response function under posture to be solved, and pass through IRCSA method inverses and obtain the response matrix of flexible junctures；(e) the milling system knife end frequency response function under posture to be solved is calculated according to RCSA methods.Forecasting Methodology proposed by the present invention, the accurate knife end frequency response function obtained under robotic milling system difference posture, realizes the accurate prediction of milling stability under robot difference posture.
Description
Technical Field
The invention relates to the field of milling equipment dynamic characteristic testing, in particular to a frequency response prediction method of a binary tree robot milling system based on RCSA.
Background
With the rapid development of industrial automation and intellectualization, industrial robots are increasingly applied to grinding, milling, polishing, drilling and boring of large-scale complex curved surface parts such as marine propellers, aircraft skins, aircraft engine blades and rocket wall barrels due to the advantages of high cost performance, large working space range, high flexibility and the like. Compared with general CNC equipment, the robot machining system has the characteristics of low rigidity and obvious dependence on rigidity pose, and the performance of the robot in the machining field is seriously limited to be exerted and improved.
Under the influence of low rigidity of the robot, the robot milling system is easy to vibrate in the milling process, so that the processing efficiency is reduced, the quality of a processed surface is influenced, the abrasion of a cutter is obviously aggravated, and the service life of the robot milling system is shortened. The tool end frequency response is an important parameter for analyzing the flutter stability limit of the milling system, the accuracy of the tool end frequency response is directly related to the reasonability of final milling process parameter determination, and the improvement of the milling quality and efficiency of the robot is further influenced.
The method for predicting the tool end frequency response of the milling system mainly aims at numerical control machines at present, and because the tool end frequency response of the machine tool does not change greatly along with the position, the tool end frequency response changes of different tools, clamping lengths and main shaft rotating speeds are analyzed mostly on the basis of an RCSA coupling method or a component modal synthesis method, and the tool end frequency responses of the machine tool in different postures and different positions are predicted by rare people. In the aspect of predicting the tool end frequency response of the robot milling system, the main method is to establish a finite element model of the robot, identify relevant dynamic parameters through experiments, and finally predict the tool end frequency response of the robot milling system in different poses, for example, the documents "mouswavi S, Gagnol V, Bouzgarrou B C, et. 181-.
In order to solve the problems, a method for quickly predicting the end frequency response of the cutter, which is convenient to operate and high in prediction precision, is urgently needed in the field of robot milling.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides a frequency response prediction method of a binary tree robot milling system based on RCSA, through carrying out hammering experiments on robot spindle-tool handle sub-structures under 32 different postures of a robot, a robot spindle-tool handle sub-structure response matrix under any given posture is predicted by using the binary tree frequency response prediction method based on RCSA, and by combining a tool sub-structure finite element analysis model, tool end frequency response functions under different postures of the robot milling system can be accurately identified, so that the technical problems of complex tool end frequency response prediction operation and low prediction precision are solved.
In order to achieve the above object, according to the present invention, there is provided a method for predicting a frequency response of a binary tree robot milling system based on RCSA, the method comprising the steps of:
(a) dividing a six-axis milling system to be processed into a substructure A, a substructure B and a flexible joint part for connecting the substructure A and the substructure B, wherein the substructure A is a cutter, the substructure B comprises a robot, a main shaft and a cutter handle, three points are set on the substructure A at will, namely a point 1, a point 2 and a point 3a, two points are set on the substructure B at will, namely a point 4 and a point 3B, wherein the point 3a and the point 3B are the intersection points of the substructure A and the substructure B, and two angles of 0 and theta are selected at each joint of the shaft 2-the shaft 6 of the robot respectively, so that 32 postures of the robot are obtained;
(b) establishing a main shaft coordinate system on the substructure B, performing a hammering experiment on the substructure B under each attitude in the main shaft coordinate system respectively for the 32 attitudes to obtain frequency response functions corresponding to two points of the substructure B under each attitude, simultaneously storing the frequency response functions according to a full binary tree, obtaining modal parameters corresponding to the frequency response functions by using a modal theory, establishing a modal parameter standardization relational expression (I) for converting a theta angle to 90 degrees to realize the orthogonalization of the modal parameters of each joint so as to obtain the modal parameters under the orthogonal attitude, establishing a relational expression (II) between the orthogonal attitude and the modal parameters of the attitude to be solved so as to obtain the modal parameters of the attitude to be solved, and thus obtaining a response matrix of the substructure B at a position of 3B under the attitude to be solved;
(c) establishing a finite element model of the substructure A in a main shaft coordinate system, establishing a cutter coordinate system on the substructure A, and performing a hammering experiment under the cutter coordinate system to obtain a frequency response function of each endpoint on the substructure A under the cutter coordinate system, establishing a relational expression (III) of the frequency response function and material parameters of the substructure A, so as to obtain the material parameters of the substructure A, and bringing the material parameters into the finite element model to obtain a frequency response function and a response matrix of the substructure A in the main shaft coordinate system;
(d) clamping the substructure A on a substructure B to form an integral structure of a milling system, performing a hammering experiment on the substructure B to obtain a frequency response function of the integral structure under the to-be-solved posture, solving by using the frequency response function at the point 3B of the substructure B obtained in the step (B) to obtain a response matrix at the point 3B of the substructure B, establishing a relational expression (IV) among the frequency response function of the integral structure, the frequency response function A of the substructure obtained in the step (c), the response matrix at the point 3B of the substructure B and the response matrix at the point 3a of the flexible joint under the to-be-solved posture by using an RCSA method, and calculating to obtain a response matrix part at the point 3a of the flexible joint under the to-be-solved posture;
(e) and (3) performing coupling calculation on the response matrix of the substructure B at the position 3B under the attitude to be solved obtained in the step (B), the response matrix of the substructure A obtained in the step (c) and the response matrix part of the joint part at the position 3a under the attitude to be solved in the step (d) according to an RCSA theory, so as to obtain the response matrix of the overall structure at the position 1 under the attitude to be solved, and thus completing the frequency response prediction of the robot milling system.
Further preferably, in step (b), said expression (one) is preferably performed as follows,
wherein a is cos2θ,b＝sin2θ，Andrepresenting the frequency response order r modal mass, modal damping and modal stiffness at node 1 in the α attitude, α being 0 °, θ or 90 °, respectively.
Further preferably, in step (b), said series (two) is preferably carried out according to the following,
wherein,respectively expressed in the attitude to be solved theta*The frequency response of the lower node 1 is the nth order modal mass, modal damping and modal stiffness.
Further preferably, in step (c), the relation (III) is preferably performed as follows,
wherein U (X) is an objective function,is the frequency response function of the substructure a in the tool coordinate system that exerts a force in the y-direction of node i or j and picks up at the y-direction of node i or j,is the frequency response function obtained by simulation of the tool parameters of the substructure a in the tool coordinate system, i is 1,2 or 3a, j is 1,2 or 3a, and the force is applied in the y direction of the node i or j and the frequency response function is picked up in the y direction of the node i or j.
Further preferably, in step (d), the relational expression (IV) is performed as follows,
wherein R is3b3bIs the response matrix, R, of the substructure B excited at the point 3B and picked up at the point 3B3a3aIs the response matrix, R, of the substructure A excited at the point 3a and picked up at the point 3aJIs a flexible joint response matrix, R, of substructure A and substructure B3a,JRepresents R3a3aAnd RJIntermediate variables of the sum, no practical significance, h11、h12And h22H3a1Is the frequency response function of the overall structure at the end points 1,2, H3a1、N3a1、H3a2、N3a2、H11、H12And H22Is the frequency response function of the substructure A, D is the sum of the response matrices, y1，y2And y3Is the element in the sum of the response matrices.
Further preferably, in step (e), the response matrix G at the point 1 of the whole structure under the pose to be solved11It is preferably calculated according to the following expression,
G11＝R11-R13aD-1R3a1
wherein R is11Is the response matrix, R, of the substructure A excited at point 1 and picked up at point 113aIs the response matrix, R, of the substructure A excited at point 3a and picked up at point 13a1Is the response matrix that the substructure a excites at point 1 and picks up at point 3 a.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. according to the invention, the binary tree is adopted to store the frequency response data of each posture, a multi-axis robot pose description model is established, and the coupling of n joints is realized;
2. the invention provides a numerical method for calculating any attitude frequency response according to an orthogonal attitude experimental frequency response result by adopting an RCSA (radar cross section) method through reasonable simplification;
3. compared with the documents mentioned in the background technology, the invention does not need to identify the kinetic parameters of each mechanical arm, and has smaller sensitivity to experimental errors, thereby being simpler to realize and having higher precision.
Drawings
FIG. 1 is a flow diagram of a method for frequency response prediction constructed in accordance with a preferred embodiment of the present invention;
FIG. 2 is a flow diagram illustrating a method for frequency response prediction in accordance with a preferred embodiment of the present invention;
FIG. 3 is a schematic diagram of a substructure division of a tool-end frequency response prediction model of a robot milling system constructed according to a preferred embodiment of the present invention;
FIG. 4 is a schematic illustration of a substructure A, B and a flexible joint constructed in accordance with a preferred embodiment of the present invention;
FIG. 5 is a diagram of a binary frequency response tree arrangement for a multi-axis machining system constructed in accordance with a preferred embodiment of the present invention;
FIG. 6 is a schematic diagram of a single revolute joint robot arm modal parameter normalization constructed in accordance with a preferred embodiment of the present invention;
FIG. 7 is a diagram of a binary tree arrangement of orthogonal attitude frequency responses for a multi-axis machining system constructed in accordance with a preferred embodiment of the present invention;
fig. 8 is a force-receiving schematic view of a space beam unit constructed in accordance with a preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Fig. 1 is a flowchart of a frequency response prediction method constructed according to a preferred embodiment of the present invention, fig. 2 is a detailed flowchart of a frequency response prediction method constructed according to a preferred embodiment of the present invention, and as shown in fig. 1 and 2, a method for fast predicting a frequency response of a binary tree robot milling system based on RCSA is specifically characterized by comprising the following steps:
(a) fig. 3 is a schematic diagram of a sub-structure division of a tool-end frequency response prediction model of a robot milling system constructed according to a preferred embodiment of the present invention, and as shown in fig. 3, the whole milling system is divided into 2 sub-structures, that is: the robot-spindle-tool holder substructure (substructure B) and the tool substructure (substructure a) are connected through a flexible joint, as shown in fig. 4, nodes 1,2 and 3a are marked on the tool substructure a, and nodes 3B and 4 are marked on the robot-spindle-tool holder substructure B, wherein the distance between the nodes 1 and 2 is L, the distance between the nodes 3B and 4 is L, and the nodes 3a and 3B are on the same straight line;
(b) selecting 2 angles at each joint of the robots Axis 2-Axis 6, carrying out hammering experiment on the determined 32 postures to obtain direct and cross-point frequency response functions corresponding to the point 3B and the point 4 of the substructure B, and specifically, selecting 2 angles at each joint of the robots Axis 2-Axis 6(k 2, 3.., 6)Can confirm 2 in total5For each of 32 different poses, proceedObtaining a direct and cross-point frequency response function H corresponding to the substructure B through a hammering experiment3b3b,xx,H3b4,xx,H3b3b,yy,H3b4,yy,H3b3b,zzWherein H is3b3b,xxRepresents a frequency response function H obtained by picking up a vibration signal on the node 3b in the x direction of the hammering node 3b in the x direction of the coordinate system3b4,xxRepresenting the frequency response function obtained by picking up the vibration signal at node 3b in x-direction at node 4 in x-direction of coordinate system, and H3b3b,yyRepresents a frequency response function obtained by picking up a vibration signal on the node 3b in the y direction of the hammering node 3b in the y direction of the coordinate system, H3b4,yyRepresents a frequency response function obtained by picking up a vibration signal on the node 3b in the y direction of the hammering node 4 in the y direction of the coordinate system, H3b3b,zzA frequency response function obtained by hammering the node 3b in the z direction of the coordinate system and picking up a vibration signal in the z direction on the node 3b is represented;
(c) storing 32 groups of frequency response data according to the arrangement mode of a full binary tree, fitting the modal parameters of each group of frequency response data according to a modal theory, and calculating the modal parameters under the orthogonal attitude of the robot according to the following steps:
(1) the frequency response of each gesture is arranged according to the structure of a full binary tree, as shown in fig. 5, n layers are provided, and the number of nodes in each layer is2kEach leaf node is2nSequentially taking one from the top layer to each layer to obtain a gesture with n degrees of freedom, namely, each leaf node corresponds to a gesture;
(2) according to the mode theory, the structural frequency response function is a superposition of a plurality of independent modes, and can be represented by the following formula:
wherein N represents a modal order, and λ ═ ω/ω is determined from the results of the hammering experimentr，ωrIs the natural frequency of the r-th order mode, ξrRepresenting the damping ratio of the order of r, KerRepresenting the modal stiffness of the r-th order. The frequency corresponding to the maximum and minimum of the real part of the frequency response function H (omega) isAndthe minimum value of the imaginary part corresponds to the natural frequency omega-omegarCorresponding to a trough value of ArAfter the frequency response function is determined, all parameter values in the formula can be obtained, and the method for fitting the modal parameters of each group of frequency response functions comprises the following steps
(3) For a robotic arm having only one revolute joint, as shown in FIG. 6, the modal parameters are normalized as follows
Wherein a is cos2θ,b＝sin2θ，Andrespectively represents the frequency response of the mechanical arm at node 1 under α postures, the order of the modal mass, the modal damping and the modal stiffness, and has
Andrespectively, the frequency response of the mechanical arm at the node 1 under the α attitude is the nth order modal stiffness, modal damping ratio and natural frequency, so that the frequency response of the node 1 under the 90-degree attitude can be obtained according to the nth order modal parameterAndobtained by MP generalized inverse calculation;
(4) for a mechanical arm with n rotating joints, the orthogonal attitude modal parameter standardization calculation method comprises the following steps:
according to the arrangement sequence of the full binary tree, carrying out single rotary joint modal parameter standardization calculation on each rotary joint from 1 to n (from top to bottom), and when carrying out modal parameter standardization on the kth joint, selecting two groups of postures with the same joint except that the kth joint is different, namely posturesAnd(m1,m2,…,mne.g. enum {1,2}), whereinThe attitude can be calculated according to the single rotary joint modal parameter standardization methodAnd corresponding frequency response modal parameters. After n joints are normalized, orthogonal modal parameters of the n joints can be obtained, and the full binary tree arrangement of the n joints is shown in fig. 7.
(d) Establishing a finite element model of the cutter substructure, and optimizing to obtain a cutter material parameter according to an actual frequency response test result of a hammering experiment, so as to further calculate a frequency response function of the cutter substructure A, wherein the method for optimizing the cutter substructure A material parameter comprises the following steps:
(1) and establishing a cutter substructure A finite element analysis model considering shear deformation according to a Timoshenko beam theory. M Timoshenko beam unit mass matrixes MeStiffness matrix KeGrouping according to a finite element method to obtain an overall stiffness matrix K and an overall mass matrix M
According to the construction method of the kinetic equation, a frequency domain kinetic equation with m Timoshenko beam unit structures can be obtained, wherein H is a 6 x (n +1) dimensional square matrix,
where C is Rayleigh damping, i.e., C- α M + β K (α and β are mass and stiffness coefficients, respectively).
(2) The tool substructure is hung by a string and the endpoint frequency response function under the tool coordinate system is measured by a hammering methodAndas shown in FIG. 8, setting the material parameters E, μ, ρ, α, β to unknown quantities X, a set of X's should be found so that the simulated endpoint frequency responseWith minimal difference from experimental measurements, i.e. solving the tool material parameter problem can be transformed into an optimization problem
The optimization of the material parameters of the cutter can be carried out by utilizing a genetic algorithm or a particle swarm algorithm.
(3) Substituting the optimized cutter material parameters into the finite element model of the cutter substructure A, and calculating the frequency response function H under the principal axis coordinate system3a1,xx、N3a1,yx、H3a2,xx、N3a2,yx、H11,xx、H12,xx、H22,xx、H11,zz、H3a1,zzIn which H is3a1,xx、N3a1,yxThe tool substructure A is represented by a translation and rotation displacement frequency response function picked up in the x direction of the node 3a by applying force in the x direction of the principal axis coordinate system of the node 1, and the other frequency response functions can be analogized. (ii) a
(e) The method comprises the following steps of measuring a robot-main shaft-tool handle-tool end frequency response through an experiment, and obtaining a response matrix of a joint of the tool handle and the tool through inverse calculation by an IRCSA (inverse kinematics and control System) method, wherein the calculation process of the response matrix comprises the following steps:
(1) clamping the cutter substructure A and the robot spindle-tool handle substructure B together to form an integral milling system structure, and selecting one of 32 frequency response test attitudes Measuring the frequency response function h in the x direction respectively11,xx、h12,xx、h22,xxMeasuring the frequency response function h in the y-direction11,yy、h12,yy、h22,yyMeasuring the frequency response function h in the z-direction11,zzWherein h is12,xxThe translation displacement frequency response function picked at the X direction of the node 1 by applying force to the X direction of the end node 2 of the tool in the overall structure of the robot milling system is shown, and the other frequency response functions can be analogized.
(2) According to the RCSA theory, the tool end response matrix of the robot milling system
G11＝R11-R13aD-1R3a1
Wherein G is11Representing a response matrix, R, of a tool end of a robotic milling system excited at 1 point and picked up at 1 point11Representing the response matrix excited at node 1 and picked up at node 1 of the substructure A, in which
D＝R3a3a+R3b3b+RJ
Wherein R isJRepresenting a flexible joint response matrix. R3b3bRepresenting a response matrix, R, excited at node 3B by the substructure B and picked up at node 3B3a3aIs the response matrix that the substructure a excites at point 3a, picking up at point 3 a.
In the x or y direction of the principal axis coordinate system, there are
For R3b3b
Then the difference formula can be obtained
Thus, according to the measured H3b3b,xx,H3b4,xx,H3b3b,yy,H3b4,yyThe response matrix R of the robot main shaft-tool handle substructure in the x and y directions can be respectively calculated3b3b。
In the z direction of the principal axis coordinate system, GefAnd RuvSimplified to
Gef＝[hef,zz](e,f∈enum{1,2})Ruv＝[Huv,zz](u,v∈enum{1,2,3a,3b,4})
For R3b3b
R3b3b＝[H3b3b,zz]＝[X3b3b,zz/F3b3b,zz]
(3) The IRCSA method for solving the response matrix of the joint part comprises the following steps:
only R is available after the robot changes the posture3b3bChange is made to rewrite B to
D＝R3b3b+R3a,J(R3a,J＝R3a3a+RJ)
Because the dimensions of the response matrixes in the x direction, the y direction and the z direction are different, the solution of the response matrix of the joint part has certain difference.
In the x or y direction of the principal axis coordinate system, the overall response matrix and the substructure response matrix satisfy the following relation
Is provided with
The above equations can be transformed according to the reciprocity theorem and the vectorization operator
In the x direction, the tool end frequency response h of the robot milling system obtained by the experiment11,xx、h12,xx、h22,xxTool substructure frequency response H calculated from finite elements3a1,xx、N3a1,yx、H3a2,xx、N3a2,yx、H11,xx、H12,xx、H22,xxSubstituting the formula to obtain D-1Further substituting the robot attitude theta*R of3b3b,xxI.e. the response matrix R in the x direction can be calculated3a,J,xx(ii) a Similarly, in the y direction, the tool end frequency response h of the robot milling system obtained by the experiment11,yy、h12,yy、h22,yyTool substructure frequency response H calculated from finite elements3a1,xx、N3a1,yx、H3a2,xx、N3a2,yx、H11,xx、H12,xx、H22,xxSubstituting the formula to obtain D-1Further substituting the robot attitude theta*R of3b3b,yyCalculating to obtain a response matrix R in the y direction3a,J,yy。
IV, in the z direction of the principal axis coordinate system, the overall response matrix and the substructure response matrix satisfy the following relation
G11＝R11-R13aD-1R3a1
The tool end frequency response h of the robot milling system obtained by the experiment11,zzTool substructure frequency response H calculated from finite elements11,zz、H3a1,zzSubstituting the formula to obtain D-1Further substituting the robot attitude theta*R of3b3b,zzI.e. the response matrix R in z-direction can be calculated3a,J,zz。
R3a,JComprising components R of three directions3a,J,xx，R3a,J,yyAnd R3a,J,zz，R3a,JA response matrix representing the flexible joint, independent of the pose of the robot.
(f) According to the RCSA-based binary tree robot milling system cutter end frequency response prediction method, the modal parameters under the orthogonal attitude obtained in the step (c) are utilized to calculate any attitude theta to be solvedobjThe frequency response function of the substructure B at the points 3B, 4, and further calculating the response matrix of the substructure B at the point 3B, which has been calculatedThe process is as follows:
(1) for the mechanical arm with a single rotary joint, the modal parameters at any angle theta can be obtained from the normalized modal parameters of 0-degree and 90-degree postures according to MP generalized inverse
(2) For a mechanical arm with n rotating joints, the frequency response calculation method comprises the following steps:
giving the attitude theta of the mechanical arm to be solvedobj＝[θ1,θ2,L,θn]According to the arrangement sequence of the full binary tree, calculating the modal parameter of each rotary joint from n-1 (from bottom to top) in turn, and selecting two groups of postures with the same posture except that the kth joint is different, namely postures when the modal parameter of the kth joint is standardizedAnd(m1,m2,L,mk-1e enum {1,2}), where the k-th and subsequent joint angles coincide with a given joint angle, the k-th joint angle is 0 ° and 90 °, and the k-th and previous joint angles are orthogonal poses, and thus have 2i-1In the method, after n joints are calculated by repeatedly using a single rotating joint modal parameter calculation method, the frequency response modal parameter corresponding to the given attitude can be obtained, and the corresponding frequency response function H is further obtained through calculation3b3b,xx,H3b4,xx,H3b3b,yy,H3b4,yy。
(3) According to the difference formula, the attitude theta to be solved can be calculatedobj＝[θ1,θ2,L,θn]Response matrix R of lower robot main shaft-tool shank substructure B at 3B3b3b,xx、R3b3b,yyAnd R3b3b,zz。
(g) Coupling the response matrix of the substructure B at the position 3B, the response matrix (frequency response function) of the substructure A and the response matrix of the combination part of the tool shank and the tool according to an RCSA (Radar Cross section) method, and calculating to obtain a to-be-solved attitude thetaobj＝[θ1,θ2,L,θn]The tool end frequency response function of the robot milling system specifically comprises the following steps:
(1) calculating the response matrix R of the flexible joint part obtained by IRCSA3a,JWith the attitude θ to be solvedobj＝[θ1,θ2,L,θn]Response matrix R of robot main shaft-tool shank substructure B at 3B3b3bSubstituting the following formula
D＝R3b3b+R3a,J
(2) According to the RCSA theory, the response matrix of the tool end node 1 of the robot milling system and the response matrix of each substructure are in the following relation
G11＝R11-R13aD-1R3a1
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. A frequency response prediction method of a binary tree robot milling system based on RCSA is characterized by comprising the following steps:
(a) dividing a six-axis milling system to be processed into a substructure A, a substructure B and a flexible joint part for connecting the substructure A and the substructure B, wherein the substructure A is a cutter, the substructure B comprises a robot, a main shaft and a cutter handle, three points are set on the substructure A at will, namely a point 1, a point 2 and a point 3a, two points are set on the substructure B at will, namely a point 4 and a point 3B, wherein the point 3a and the point 3B are the intersection points of the substructure A and the substructure B, and two angles of 0 and theta are selected at each joint of the shaft 2-the shaft 6 of the robot respectively, so that 32 postures of the robot are obtained;
(b) establishing a main shaft coordinate system on the substructure B, performing a hammering experiment on the substructure B under each attitude in the main shaft coordinate system respectively for the 32 attitudes to obtain frequency response functions corresponding to two points of the substructure B under each attitude, simultaneously storing the frequency response functions according to a full binary tree, obtaining modal parameters corresponding to the frequency response functions by using a modal theory, establishing a modal parameter standardization relational expression (I), realizing the orthogonalization of the modal parameters converted from theta degrees of each joint to 90 degrees to obtain the modal parameters under the orthogonal attitudes, and establishing the orthogonal attitudes and the attitudes to be solved thetaobjObtaining a relation formula (II) of modal parameter relation so as to obtain the attitude theta to be solvedobjModal parameters and obtaining the pose to be solved theta from the modal parametersobjThe response matrix of the lower substructure B at 3B;
(c) establishing a finite element model of the substructure A in a main shaft coordinate system, establishing a cutter coordinate system on the substructure A, and performing a hammering experiment under the cutter coordinate system to obtain a frequency response function of each endpoint on the substructure A under the cutter coordinate system, establishing a relational expression (III) of the frequency response function and material parameters of the substructure A, so as to obtain the material parameters of the substructure A, and bringing the material parameters into the finite element model to obtain a frequency response function and a response matrix of the substructure A in the main shaft coordinate system;
(d) clamping the substructure A on the substructure B to form an integral structure of the milling system, and selecting any one attitude theta from the 32 attitudes*At the attitude of theta*Carrying out hammering experiment on the flexible joint part to obtain a frequency response function of the overall structure, solving by using the frequency response function at the B point 3B of the substructure obtained in the step (B) to obtain a response matrix at the B point 3B of the substructure, establishing a relational expression (IV) among the frequency response function of the overall structure, the A frequency response function of the substructure obtained in the step (c), the response matrix at the B point 3B of the substructure and the response matrix of the flexible joint part by adopting an RCSA (remote control system) method, and calculating to obtain the response matrix of the flexible joint part;
(e) according to the RCSA theory, the attitude theta to be solved obtained in the step (b)objAnd (3) performing coupling calculation on the response matrix of the lower substructure B at the position 3B, the response matrix of the substructure A obtained in the step (c) and the response matrix part of the flexible joint part in the step (d) to obtain a response matrix at the position 1 of the overall structure under the attitude to be solved, thereby completing the frequency response prediction of the robot milling system.
2. The RCSA-based binary tree robot milling system frequency response prediction method of claim 1, wherein in step (b), the expression (one) is preferably performed according to the following,
wherein a is cos2θ,b＝sin2θ，Andrepresenting the frequency response order r modal mass, modal damping and modal stiffness at node 1 in the α attitude, α being 0 °, θ or 90 °, respectively.
3. The RCSA-based binary tree robot milling system frequency response prediction method according to claim 1 or 2, wherein in step (b), the series (two) is preferably performed according to the following,
wherein,respectively expressed in the attitude to be solved thetaobjThe frequency response of the lower node 1 is the nth order modal mass, modal damping and modal stiffness.
4. The RCSA-based binary tree robot milling system frequency response prediction method according to any one of claims 1-3, wherein in step (c), the relation (III) is preferably performed according to the following,
wherein U (X) is an objective function,is the frequency response function of the substructure a in the tool coordinate system that exerts a force in the y-direction of node i or j and picks up at the y-direction of node i or j,is the frequency response function obtained by simulation of the tool parameters of the substructure a in the tool coordinate system, i is 1,2 or 3a, j is 1,2 or 3a, and the force is applied in the y direction of the node i or j and the frequency response function is picked up in the y direction of the node i or j.
5. The RCSA-based binary tree robot milling system frequency response prediction method according to any one of claims 1-4, wherein in step (d), the relation (IV) is performed according to the following,
wherein R is3b3bIs the response matrix, R, of the substructure B excited at the point 3B and picked up at the point 3B3a3aIs the response matrix, R, of the substructure A excited at the point 3a and picked up at the point 3aJIs a flexible joint response matrix, R3a,JIs the response matrix of the flexible joint, h11、h12And h22H3a1Is the frequency response function of the overall structure at the end points 1,2, H3a1、N3a1、H3a2、N3a2、H11、H12And H22Is the frequency response function of the substructure A, D is the sum of the response matrices, y1，y2And y3Is the element in the sum of the response matrices.
6. The RCSA-based binary tree robot milling system frequency response prediction method of any one of claims 1-5, wherein in the step (e), the response matrix G at the point 1 of the whole structure under the attitude to be solved is shown as the G11It is preferably calculated according to the following expression,
G11＝R11-R13aD-1R3a1
wherein R is11Is the response matrix, R, of the substructure A excited at point 1 and picked up at point 113aIs the response matrix, R, of the substructure A excited at point 3a and picked up at point 13a1Is the response matrix that the substructure a excites at point 1 and picks up at point 3 a.
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