CN-121997658-A - Cutter point dynamic characteristic analysis method for milling process of five-axis parallel-serial machine tool

Abstract

The invention discloses a cutter point dynamic characteristic analysis method in a milling process of a five-axis parallel-serial machine tool, which belongs to the technical field of the five-axis parallel-serial machine tool, and comprises the following steps of firstly carrying out system dynamics modeling on the five-axis parallel-serial machine tool, establishing a dynamics equation of a cutting system formed by a cutter and the five-axis parallel-serial machine tool in the milling process of the five-axis parallel-serial machine tool, secondly setting dynamics parameters according to the condition that the dynamics parameters can change along with the position and the posture of the parallel-serial machine tool, thirdly, setting a main shaft coordinate system, a cutter coordinate system and a workpiece coordinate system to calculate three-way dynamic milling force born by the cutter in the milling process, and fourthly, determining track influence caused by radial runout and milling vibration of the cutter according to the three-way dynamic milling force, and combining the track influence into a real movement track of the cutter. By adopting the method, the rigidity change of the five-axis parallel-serial machine tool is calculated, a corresponding structural dynamics model is established, and the dynamic characteristic estimation of the machine tool under different postures is realized.

Inventors

• ZHANG JUN
• HE ZHEN
• FANG HANLIANG
• GUO DEMIN
• LI YI

Assignees

• 福州大学

Dates

Publication Date

20260508

Application Date

20260123

Claims (5)

1. 1. A method for analyzing dynamic characteristics of a cutter point in a milling process of a five-axis parallel-serial machine tool is characterized by comprising the following steps: Firstly, carrying out system dynamics modeling on a five-axis parallel-serial machine tool, and establishing a dynamics equation of a cutting system formed by a cutter and the five-axis parallel-serial machine tool in the milling process of the five-axis parallel-serial machine tool; Step two, aiming at the condition that the dynamic parameters can be changed along with the pose of the parallel-serial machine, setting the dynamic parameters; Step three, setting a main shaft coordinate system Coordinate system of tool And a workpiece coordinate system Calculating three-way dynamic milling force applied to the cutter in the milling process; And step four, determining the track influence caused by radial runout and milling vibration of the cutter according to the three-way dynamic milling force, and combining the track influence into the real motion track of the cutter.
2. 2. The method for analyzing the dynamic characteristics of the tool tip in the milling process of the five-axis hybrid machine tool according to claim 1 is characterized in that in the first step, a dynamic equation of a cutting system formed by a cutter and the five-axis hybrid machine tool is given as follows: ; In the above-mentioned method, the step of, Representing a mass matrix of the cutting system, Representing the damping matrix of the cutting system, Representing a stiffness matrix of the cutting system, Expressed as the vibrational response of the cutting system at time t, Denoted as cutting force actuation of the cutting system at time t, Represented as Is used as a first derivative of (a), Represented as Is a second derivative of (c).
3. 3. The method for analyzing the dynamic characteristics of the tool point in the milling process of the five-axis parallel-serial machine tool according to claim 2 is characterized in that in the second step, the specific process of setting the dynamic parameters is as follows: According to the structural characteristics of the five-axis parallel-serial machine tool, the five-axis parallel-serial machine tool is equivalent to a space mechanical system consisting of a variable cross-section beam entity and a revolute pair, in the process of modeling the structural power of the machine tool, the following assumption is made that ① assumes that each substructure can be equivalent to the variable cross-section beam entity, the mass and rigidity matrix of each substructure is built by dividing the beam entity into a series of variable cross-section space beam units and adopting a finite element method, ② assumes that the sliding component of each branched chain is fixedly connected with the machine tool, and regards the five-axis parallel-serial machine tool with different poses as a series of transient structures, ③ assumes that the ideal assembly relation is formed between each variable cross-section beam entity, and ignores the influence of installation gaps, damping and friction force in the revolute pair, and the dynamic parameters of the five-axis parallel-serial machine tool comprise the mass matrix Damping matrix And stiffness matrix Because the dynamic parameters of the five-axis parallel-serial machine tool can be changed along with the change of the pose of the parallel-serial machine due to the structural characteristic of the five-axis parallel-serial machine tool, the dynamic parameters of the five-axis parallel-serial machine tool are set, and the setting process is as follows: the movable platform system of the five-axis parallel-serial machine tool comprises an upper movable platform, a lower movable platform, a cutter-spindle module and a plurality of branched chains Each branched chain The system comprises three substructures of the same sliding component, a middle connecting rod and a tail end connecting rod, a movable platform system of a five-axis parallel-serial machine tool is subdivided into six substructures, and each substructures is analyzed and a corresponding mass and rigidity matrix is established based on a beam unit theory; Dividing the upper platform into two parts according to the structural characteristics of the upper moving platform and the lower moving platform Each unit node divides the lower platform into Each unit node has 6 degrees of freedom, so that the dimensions of the rigidity matrix and the mass matrix of the upper moving platform are The dimensions of the rigidity matrix and the mass matrix of the lower moving platform are ; In the tool-spindle module, the tool is fixed on the machine tool spindle through the collet chuck, so the tool and the machine tool spindle are regarded as a whole and divided into Each unit node has dimensions of mass and rigidity matrix Wherein the node corresponding to the joint of the cutter and the main shaft is The corresponding node of the joint of the cutter-spindle module and the upper moving platform is ; The sliding component comprises a plurality of parts, and the parts are connected by bolts and the like, so that the sliding component is regarded as a whole and divided into the following parts according to the structural characteristics of the sliding component Each unit node has dimensions of mass and rigidity matrix ; According to the structural characteristics of the middle connecting rod and the tail connecting rod, the two connecting rods are respectively divided into And Each unit node, therefore, the dimensions of the mass and stiffness matrix of the intermediate link are The dimensions of the mass and stiffness matrix of the end link are ; Through the analysis, the rigidity matrix of the upper moving platform, the lower moving platform, the cutter-spindle module, the middle connecting rod and the tail end connecting rod 、 、 、 And Collectively expressed as: ; in the formula, Corresponding beam unit number Respectively equal to 、 、 、 And ; Representing the first of the substructures Sub-matrices of the individual beam unit stiffness matrices, the subscript pp of which is a calculation index representing the positions of the sub-matrices in the beam unit stiffness matrices; Mass matrix of upper moving platform, lower moving platform, cutter-spindle module, intermediate link and end link 、 、 、 And The unified representation is as follows: ; in the formula, Corresponding beam unit number Respectively equal to 、 、 、 And ; Representing the first of the substructures Sub-matrices of the individual beam unit mass matrices, the subscript pp of which is a calculation index representing the position of the sub-matrix in the beam unit mass matrix; Due to the sliding assembly beam unit at the node Is connected in parallel, and is regarded as a beam entity consisting of a series of beam units connected in series and in parallel, the stiffness matrix of which is based on a hydrostatic equilibrium equation The correction is as follows: ; Mass matrix of sliding assembly The correction is as follows: ; According to the structural attribute of the five-axis parallel-serial machine tool, the mass matrix and the rigidity matrix of each substructure are assembled into the mass matrix and the rigidity matrix of the machine tool based on the same joint assembly method, and the mass matrix and the rigidity matrix of each substructure are consistent in structural form and assembly form, so that the assembly process of the rigidity matrix of the five-axis parallel-serial machine tool is as follows: At each branch In the middle, the sliding component and the middle connecting rod, and the middle connecting rod and the tail end connecting rod are respectively connected through a revolute pair And Connecting and rotating the pair And Corresponding rotation angle of (a) is And To assemble the stiffness matrix of the branched system in the same reference frame, the stiffness matrix of the intermediate link is From revolute pair Reference coordinate system of (2) Conversion to branched chain coordinate system In (3) for each branched chain Stiffness matrix of intermediate link The calculation is as follows: ; In the above-mentioned method, the step of, Is that Winding machine Rotation of the shaft Is to matrix the rigidity of the end link From revolute pair Reference coordinate system of (2) Conversion to branched chain coordinate system In (3) for each branched chain Rigidity matrix of connecting rod between its ends Expressed as: ; In the above-mentioned method, the step of, Is that Winding machine Rotation of the shaft Specifically, the coordinate transformation matrix of (a) is: ; in the above formula, alpha y is the angle rotating around the Y axis, and the specific angle value is replaced during calculation; The sliding component, the middle connecting rod and the tail connecting rod are all connected by a revolute pair, and the rotation axes are all in a branched chain coordinate system A kind of electronic device Axis parallel, based on joint assembly method to respectively matrix rigidity 、 And Equivalent deformation into 、 And Each branched chain Stiffness matrix of (2) Expressed as: ; In the above-mentioned method, the step of, 、 And Respectively stiffness matrix 、 And Specifically: ; In the above-mentioned method, the step of, And Respectively a unit matrix and a zero matrix, the subscripts of which are given by And Respectively representing the row number and column number of matrix, and the rigidity matrix of branched chain From a branched chain coordinate system Conversion to a mobile platform system coordinate system The formula is as follows: ; In the above-mentioned method, the step of, Representing a dynamic platform system coordinate system The stiffness matrix of the lower branch i, Representing a dynamic platform system coordinate system Relative to the machine tool static coordinate system Is used for the transformation matrix of the (c), Representing a coordinate system The angle of rotation about the z-axis, Indicating the roll angle of the roll, Indicating the roll angle of the roll, Is a coordinate system Winding machine The coordinate transformation matrix of the shaft rotation is specifically: ; In the above formula, alpha z is the angle of rotation around the z axis, and the specific angle value is replaced during calculation; Due to the nodes of the upper moving platform Node with tool spindle module Are connected in parallel, so that the rigidity matrix of the two is that Expressed as: ; in the above, superscripts Representing first matrix Middle node And node The corresponding column vectors are interchanged, and then the nodes are replaced To the point of The corresponding column vector is translated to the node To the point of Is a position of (2); And Respectively is And Specifically: ; Matrix the rigidity Converting the upper moving platform coordinate system into the coordinate system of the moving platform system to obtain The formula is as follows: ; ; ; In the above-mentioned method, the step of, Representing the upper moving platform coordinate system Relative to the mobile platform system coordinate system Is used for the transformation matrix of the (c), Representing the upper moving platform coordinate system Relative to the mobile platform system coordinate system Is fixed at the upper part of the platform Node with lower moving platform Is in rotary connection with the rotary shaft, and the rotary shaft is a movable platform system Shafts, respectively stiffness matrices based on joint assembly method And Equivalent deformation into And Stiffness matrix of the mobile platform system Expressed as: ; in the formula, And Respectively stiffness matrix And Specifically: ; in the formula, Is a rigidity matrix And satisfy the following ; Each branched chain is respectively connected with the rotary pair Is connected with a movable platform system and is provided with a revolute pair And Is a coordinate system A kind of electronic device A shaft(s), Revolute pair And Is a coordinate system A kind of electronic device Shafts for respectively arranging rigidity matrix of dynamic platform system based on joint assembly method Stiffness matrix of each branched chain 、 、 And Equivalent deformation into 、 、 、 And Stiffness matrix of machine tool The representation is: ; in the formula, 、 、 、 And Respectively stiffness matrix 、 、 、 And Specifically: ; in the formula, Stiffness matrix for dynamic platform system Is of the dimension of (1) ; Is a stiffness matrix of a branched chain system Is of the dimension of (1) ; Obtaining a mass matrix of the machine tool based on a joint assembly method by adopting the same method as the rigidity matrix Due to the nodes in the sliding assembly Sum node Is fixedly connected with the machine tool, and the corresponding generalized displacement is zero, so that the node Sum node The corresponding rows and columns in the mass and rigidity matrix are eliminated in the process of solving the motion differential equation, and because the zero vector expansion is carried out on the beam unit mass and rigidity matrix in the process of assembling the revolute pair mass and rigidity matrix, when one row or one column in the mass and rigidity matrix of the machine tool is the zero vector, the row and the column are eliminated, and finally the mass matrix of the five-axis hybrid machine tool is obtained And stiffness matrix Considering the effect of damping in a machine tool, its damping matrix is as follows: ; In the above-mentioned method, the step of, And To calculate a constant and greater than 0.
4. 4. The method for analyzing the dynamic characteristics of the tool tip point in the milling process of the five-axis hybrid machine tool according to claim 3 is characterized in that in the third step, the three-way dynamic milling force applied to the tool in the milling process is determined, and the specific process is as follows: at any time t in the milling process, radial runout of the cutter can cause the cutter tip to be positioned relative to a given machining track Shaft and method for producing the same Dynamic offset distance in axial direction And The calculation formula is as follows: ; In the above-mentioned method, the step of, The eccentric distance of the radial runout of the cutter is shown, Representing the angle of rotation of the tool runout, taking into account the coordinate system of the tool about the workpiece during five-axis milling Shaft and method for producing the same Roll angle of shaft And front inclination angle The real coordinates of the real machining track of the cutter milling on the workpiece coordinate system are 、 And The formula is as follows: ; ; ; In the above-mentioned method, the step of, And Respectively represent the winding of the cutter Shaft and method for producing the same A rotation matrix of axes; 、 And Respectively, the coordinates of a given processing track in a workpiece coordinate system and the coordinates of a given processing track in a tool coordinate system In the pair of serial numbers The height is Is a blade with any point on the blade Coordinate position of (2) 、 And The formula of (2) is as follows: ; In the above-mentioned method, the step of, Indicating the effective milling radius of the tool, The edge lag angle is expressed, and the calculation formula is as follows: ; ; in the calculation formula of (a), The radius of the tool is indicated, In the calculation formula of the knife angle radius and the knife edge lag angle, N represents the number of teeth, Representing the helix angle of the cutter; for sequence number of Is of axial height of Points of (2) Calculating the radial runout and milling vibration of the tool under the influence of the comprehensive tool A shaft(s), Shaft and method for producing the same True coordinate position of axis 、 And The following are provided: ; In the above-mentioned method, the step of, Is a rotation matrix around the Z axis; The rotation angle of the cutter is the rotation angle of the main shaft Related to; 、 And Three-way milling vibration of the tool nose point is respectively carried out; The instantaneous undeformed cutting thickness corresponding to the blade infinitesimal is solved by using milling geometric simulation, firstly, the workpiece is divided into a series of workpiece infinitesimal, the discrete direction is that The shaft and the interval are arranged as When discretely spaced Small enough, the workpiece element is considered as a spatial cylinder whose side geometry is constant in the direction of the discrete axis, and therefore considered as a series of boundary points Continuous and closed boundary curves are formed, and due to the side inclination of the tool during milling And front inclination angle An included angle is formed between the axial rotation plane of the cutter and the workpiece infinitesimal plane, so that the axial rotation plane of the cutter is projected to the workpiece infinitesimal plane, the space contact problem between the cutter and the workpiece is simplified into a plane contact problem, and the plane cutting thickness of the blade infinitesimal is solved by a numerical method ; Thus, for any moment of the five-axis milling process Dynamic chip thickness of blade infinitesimal according to geometrical relation between axial rotation plane and projection plane of blade The formula of (2) is as follows: ; In the above, i is the i-th cutting edge point, and the intersection point Is the intersection point of the axial tangential plane of the cutter and the central axis of the cutter Is the intersection point of the horizontal section of the cutter and the central shaft of the cutter, Is the intersection point To the intersection point Based on the micro-element milling force model, calculating tangential force of the blade micro-element Radial force And axial force The following are provided: ; In the above-mentioned method, the step of, 、 、 Shear force coefficients of tangential force, radial force and axial force, respectively; 、 、 plow-cutting force coefficients of tangential force, radial force and axial force respectively; 、 The axial cutting width and the cutting arc length of the blade are respectively the cutting width and the cutting arc length of the blade, the milling force born by all the blade elements is converted into a workpiece coordinate system, and the three-way dynamic milling force born by the cutter is obtained through numerical integration 、 And The method comprises the following steps: ; ; In the above-mentioned method, the step of, The immersion angle of the blade infinitesimal is indicated.
5. 5. The method for analyzing the dynamic characteristics of the tool tip in the milling process of the five-axis hybrid machine tool according to claim 4, wherein in the fourth step, the track influence caused by radial runout and milling vibration of the tool is determined according to the three-way dynamic milling force, and the track influence is combined into the real motion track of the tool, and the method comprises the following specific steps: By using The dynamic equation of the cutting system is solved by a numerical discrete method to obtain the vibration response of the system, and the initial state is defined And All are zero, and a proper time increment is selected And numerical integration parameter phi, calculate integration process constant 、 And The following are provided: ; Then any one When (1) The formula of (2) is as follows: ; ; After the solution is completed, extracting the reference point of the tail end of the cutter And uses the elastic displacement vector of the cutting system as a milling vibration response of the cutting system, and the elastic displacement vector is used in the cutting tool A shaft(s), Shaft and method for producing the same True coordinate position of axis 、 And And superposing the motion information in the real motion trail of the cutter.

Description

Cutter point dynamic characteristic analysis method for milling process of five-axis parallel-serial machine tool Technical Field The invention relates to the technical field of five-axis parallel-serial machine tools, in particular to a cutter point dynamic characteristic analysis method in a milling process of a five-axis parallel-serial machine tool. Background Five-axis parallel-serial machine tool has become important equipment for manufacturing large complex workpieces due to higher flexibility and larger working space. The multiple link structure, while maintaining wide area coverage, tends to be accompanied by lower and variable system stiffness compared to conventional rigid machine tools. The rigidity change of the milling cutter can directly influence the cutting force and vibration response in the milling process, so that the further improvement of the machining precision and the surface quality is restricted. Therefore, the rigidity characteristics of the five-axis parallel-serial machine tool under different processing pose and the coupling effect of the rigidity characteristics on milling behaviors are deeply disclosed, and the method has important significance for optimizing cutting parameters, predicting system stability and realizing high-precision processing. At present, the methods commonly used for predicting the rigidity of a robot can be divided into two main types, namely an experimental fitting method and a structural dynamics method. The experimental fitting method obtains parameters through modal testing, and then utilizes means such as regression, convolutional neural network, migration learning and the like to construct a prediction model. The method is visual and easy to verify, but has large experimental quantity and high cost, and is difficult to cover the prediction of the frequency response function under the full working space. The structural dynamics rule relies on physical constitutive equation to construct mass, damping and stiffness matrix and predict dynamic response, and common methods include finite element method and substructure synthesis method. The method combines CAD/CAE to realize high-fidelity simulation, but is widely used for theoretical verification and local analysis because of frequent grid repainting and large calculated amount of gesture change, and the method is used for obviously improving efficiency while ensuring accuracy by dividing a connecting rod into beam units and adopting reduced-order processing to assemble an integral dynamics equation, so that the method has been successfully applied to rigidity and low-order modal analysis of various parallel and five-axis series-parallel machine tools. At present, the rigidity prediction research on the five-axis parallel-serial machine tool body is very mature. However, in the milling process, besides the influence of system rigidity, the five-axis hybrid machine tool also has a nonlinear dynamic regeneration effect, which can cause the problems of complex milling vibration and the like. The precondition for predicting milling dynamics is to build a model of the cutting dynamics. However, the rigidity change of the robot body is not considered in the currently established dynamic model, and the dynamic model is mostly regarded as a constant and is obtained in an experimental mode, so that the milling behavior cannot be accurately reflected. Disclosure of Invention The invention aims to provide a cutter point dynamic characteristic analysis method for a milling process of a five-axis hybrid machine tool, which is characterized in that a structural dynamics model of a novel five-axis hybrid machine tool is established by considering the rigidity change of a robot body, the natural frequency of the machine tool and the vibration response of the machine tool under unit step load are analyzed, the dynamic characteristic estimation of the machine tool under different postures is realized, a dynamic model of a milling system is established by combining workpiece material removal simulation on the basis of considering the milling regeneration effect and the dynamic characteristic of the machine tool, and the prediction of milling force, milling vibration and shape and position errors in complex curved surface processing is realized. In order to achieve the purpose, the invention provides a cutter point dynamic characteristic analysis method for a milling process of a five-axis parallel-serial machine tool, which comprises the following steps: Firstly, carrying out system dynamics modeling on a five-axis parallel-serial machine tool, and establishing a dynamics equation of a cutting system formed by a cutter and the five-axis parallel-serial machine tool in the milling process of the five-axis parallel-serial machine tool; Step two, aiming at the condition that the dynamic parameters can be changed along with the pose of the parallel-serial machine, setting the dynamic parameters; Step three, setting a main sha