CN111291479A - Method for predicting milling stability of series-parallel machine tool - Google Patents
Method for predicting milling stability of series-parallel machine tool Download PDFInfo
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Abstract
The invention discloses a method for predicting milling stability of a series-parallel machine tool, which comprises the following steps: the method comprises the following steps of dividing the whole series-parallel machine tool system into a cutter, a cutter handle, a main shaft and a parallel/parallel series-parallel mechanism, wherein the cutter, the cutter handle and the main shaft are used as a first substructure, and the parallel/parallel series-parallel mechanism is used as a second substructure; measuring and acquiring frequency response functions of the first substructure and the second substructure, and acquiring a tool nose point frequency response function; establishing a milling kinetic equation under a physical coordinate system; converting a milling kinetic equation under a physical coordinate system into a milling kinetic equation under a modal coordinate system; solving a milling kinetic equation under a modal coordinate system to obtain a state transition matrix; judging the characteristic value of the state transition matrix, and drawing a stability lobe graph; and carrying out milling stability prediction on the hybrid machine tool system according to the stability lobe graph. The method comprehensively considers the influence of the low-order dynamic characteristic and the medium-order dynamic characteristic of the parallel mechanism, and can predict the milling stability of the parallel machine more accurately.
Description
Technical Field
The invention relates to the technical field of machine tool manufacturing, in particular to a method for predicting milling stability of a series-parallel machine tool.
Background
Since the 21 st century, the parallel mechanism is more and more widely applied in the industry due to the advantages of high rigidity, high precision, bearing capacity and the like. The parallel machine tool is used as an innovation of a machine tool structure, has better performance in the aspects of precision and rigidity compared with the traditional machine tool in theory, has light weight and good processing flexibility, and has attracted wide attention at home and abroad. However, the practical and industrialized production of the existing series-parallel machine tool at home and abroad is very limited. The static performance, the dynamic performance and the like of the domestic and foreign hybrid machine tools have more or less problems. At present, the static rigidity and dynamic characteristics of the machine tool obtained through theoretical analysis and simulation have large differences with actual measurement, the design requirements cannot be met, and the problems which are not found or solved in the aspects of static and dynamic characteristic prediction and the like exist.
Chatter is a very strong self-excited vibration generated between a tool and a workpiece in a metal cutting process, is excited by a cutting force and maintains vibration not to be attenuated, is a main vibration phenomenon in a machine tool machining process, and has great influence on machining precision, tool life and the like. In the aspect of measuring milling stability of a machine tool, the traditional machine tool is widely researched, the stability of a cutter-cutter handle-main shaft system is mainly researched for the vibration stability of the traditional machine tool, the flexibility of a main shaft, a cutter handle and a cutter, the characteristics of the joint surfaces of the main shaft, the cutter handle and the cutter handle, and the like are mainly considered, and the vibration problem caused by the structure of the machine tool is basically not considered. The serial machine tool has mature structural design and reasonable structural parameters, and can ensure that the serial machine tool has better static rigidity and dynamic characteristics, so that the machine tool structure basically cannot vibrate in the machining and milling process.
However, for the parallel machine tool, due to the configuration characteristic of the parallel mechanism, the static rigidity characteristic of the parallel mechanism is changed greatly under different postures, and meanwhile, most of the parallel machine tool structures are novel structures, the structural design and optimization work of each part is incomplete, and the assembly method and the assembly process are not standard, so that the structural rigidity of the parallel machine tool is not ideal. Therefore, based on the existing machine tool milling stability prediction method, the difference between the static rigidity and the dynamic characteristic of the measured series-parallel machine tool and the actual value is large.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method for predicting milling stability of a hybrid machine tool, so as to solve the problem that the prediction result of the conventional stability prediction method has a large deviation from the actual result.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a method for predicting milling stability of a series-parallel machine tool, which comprises the following steps:
the method comprises the following steps of dividing the whole series-parallel machine tool system into a cutter, a cutter handle, a main shaft and a parallel/parallel series-parallel mechanism, wherein the cutter, the cutter handle and the main shaft are used as a first substructure, and the parallel/parallel series-parallel mechanism is used as a second substructure;
measuring and obtaining frequency response functions of the first substructure and the second substructure, and obtaining a tool nose point frequency response function by using an admittance coupling method;
establishing a milling kinetic equation under a physical coordinate system with multiple degrees of freedom in two orthogonal directions by taking a milling workpiece as a rigid body and a parallel-series machine tool system as a flexible body;
converting a milling kinetic equation under a physical coordinate system into a milling kinetic equation under a modal coordinate system;
solving a milling kinetic equation under a modal coordinate system by adopting a full discrete time domain method to obtain a state transition matrix;
judging the characteristic value of a state transition matrix according to a Frokay theory to obtain the stable state of the series-parallel machine tool system, and drawing a stability lobe graph;
and carrying out milling stability prediction on the hybrid machine tool system according to the stability lobe graph.
Preferably, the milling kinetic equation in the physical coordinate system is as follows:
wherein the content of the first and second substances,
a quality matrix representing the series-parallel machine tool system,
a damping matrix representing the series-parallel machine tool system,
representing the stiffness matrix of the series-parallel machine system, fx (t) representing the cutting force vector in the x-direction, Fy(t) represents a cutting force vector in the y direction, t represents time, x (t) represents displacement in the x direction, and y (t) represents displacement in the y direction.
Preferably, the milling kinetic equation in the modal coordinate system is as follows:
wherein M represents a mass matrix of the series-parallel machine tool system, C represents a damping matrix of the series-parallel machine tool system, K represents a stiffness matrix of the series-parallel machine tool system, q (t) represents displacement in a modal coordinate system,
representing the velocity in the modal coordinate system,
represents the acceleration in the modal coordinate system, apIndicating axial depth of cut, Kq(t) represents a force coefficient matrix, fq(T) represents the static force matrix, TcIndicating the tooth pass frequencyAnd (4) rate.
Preferably, the obtained state transition matrix Φ is as follows:
Φ＝Dm-1Dm-2…D1D0
where Φ represents a state transition matrix and D represents an intermediate variable matrix calculated using a full discrete time domain method.
Preferably, in the step of establishing a milling kinetic equation in a physical coordinate system orthogonal to the two directions of multiple degrees of freedom, the milling cutting force is obtained by the following formula:
wherein, Fx(t) x-direction milling cutting force, Fy(t) represents a milling cutting force in the y-direction, apThe axial cutting depth is indicated as the axial depth,
a matrix of force coefficients is represented by a matrix of force coefficients,
representing the static force matrix, T representing the time, TcRepresenting the tooth passing frequency, x1(t) x-direction displacement of the center point of the tool at time t, y1(t) represents the y-direction displacement of the tool center point at time t.
Preferably, in the step of obtaining the nose point frequency response function by using an admittance coupling method, the dynamic characteristics of the junction surfaces of the first substructure and the second substructure are inversely obtained by using the admittance coupling method.
Preferably, the step of measuring and acquiring the frequency response functions of the first substructure and the second substructure comprises:
arranging an acceleration sensor at a position to be measured;
knocking at the position to be detected by adopting a force hammer, and obtaining acceleration information of the position to be detected by a signal acquisition device;
and processing the acceleration information and converting the acceleration information in a frequency domain by using Fourier transform to obtain a frequency response function of the position to be measured.
Preferably, in the step of determining the eigenvalue of the state transition matrix to obtain the stable state of the hybrid machine tool system, if the moduli of all eigenvalues of the state transition matrix are less than 1, the hybrid machine tool system is determined as a stable system.
Preferably, the milling kinetic equation under the modal coordinate system is solved by using a full discrete time domain method, and the step of obtaining the state transition matrix includes:
acquiring a low-order modal parameter and a high-order modal parameter by a modal parameter identification method;
and acquiring a state transition matrix according to the low-order modal parameters and the high-order modal parameters.
Compared with the prior art, the invention has the following advantages and beneficial effects:
according to the invention, the whole series-parallel machine tool system is divided into two substructures, so that the influence of the low-order dynamic characteristics of the parallel/parallel series-parallel mechanism and the medium-order and high-order dynamic characteristics of parts such as a cutter and the like is comprehensively considered in the process of predicting the milling stability, and the accuracy of predicting the milling stability of the series-parallel machine tool is improved.
Drawings
FIG. 1 is a schematic flow chart of a milling stability prediction method of a hybrid machine tool in the invention;
FIG. 2 is a schematic diagram of the subdivision of the series-parallel machine tool system according to the present invention;
fig. 3 is a diagram showing the verification result of the milling stability prediction method of the present invention.
Detailed Description
The embodiments of the present invention will be described below with reference to the accompanying drawings. Those of ordinary skill in the art will recognize that the described embodiments can be modified in various different ways, or combinations thereof, without departing from the spirit and scope of the present invention. Accordingly, the drawings and description are illustrative in nature and not intended to limit the scope of the claims. Furthermore, in the present description, the drawings are not to scale and like reference numerals refer to like parts.
Fig. 1 is a schematic flow chart of a method for predicting milling stability of a hybrid machine tool in the present invention, and as shown in fig. 1, the method for predicting milling stability of a hybrid machine tool provided by the present invention includes the following steps:
step S1, the whole parallel-serial machine tool system is divided into four parts, namely, the tool holder 12, the spindle 11, and the parallel/parallel-serial mechanism, and the parallel/parallel-serial mechanism is a structural combination of the parallel-serial system except the tool, the tool holder 12, and the spindle 11. When the milling stability of the hybrid machine tool is predicted, the tool 13, the tool holder 12, the main shaft 11 and the parallel/parallel hybrid mechanism are divided into two substructures, fig. 2 is a substructure division schematic diagram of the hybrid machine tool system of the present invention, and as shown in fig. 2, the tool 13-the tool holder 12-the main shaft 11 is used as a first substructure 1, and the parallel/parallel hybrid mechanism is used as a second substructure 2, wherein the first substructure 1 and the second substructure 2 are elastically coupled.
Step S2, measuring and acquiring frequency response functions of the first substructure 1 and the second substructure 2, and obtaining a nose point frequency response function by using an admittance Coupling method (RCSA). The frequency response function of the first substructure 1 reflects the medium-high order dynamic characteristic of the series-parallel machine tool system, and the frequency response function of the second substructure 2 reflects the low order dynamic characteristic of the series-parallel machine tool system. Because the low-order dynamic characteristics reflected by the parallel/parallel hybrid mechanism have larger influence on the milling stable region low-rotation speed section in the milling process of the hybrid machine tool, the influence of the low-order dynamic characteristics and the medium-order dynamic characteristics is comprehensively considered when the milling stability of the hybrid machine tool is predicted, and the accuracy of stability prediction can be improved.
And step S3, establishing a milling kinetic equation under a multi-degree-of-freedom physical coordinate system in two orthogonal x-y directions by taking the milling workpiece as a rigid body and the parallel-serial machine tool system as a flexible body. The milling workpiece is a rigid workpiece which can be milled and can be a plane, a groove, various forming surfaces (such as a spline, a gear and a thread) and the like of a part.
And step S4, converting the milling kinetic equation in the physical coordinate system into the milling kinetic equation in the modal coordinate system.
And step S5, solving a milling kinetic equation under the modal coordinate system by adopting a full discrete time domain method, and acquiring a state transition matrix.
And step S6, judging the characteristic value of the state transition matrix according to Floquet theory (Floquet theory), obtaining the stable state of the hybrid machine tool system when the spindle rotating speed and the axial cutting depth are given, and drawing a stable lobe graph. Because the state transition matrix is related to the rotating speed of the main shaft and the axial cutting depth, when the rotating speed of the main shaft and the axial cutting depth are changed, the stability of the system at the moment can be judged by judging the characteristic value of the state transition matrix in the state corresponding to different state transition matrices, and therefore the stability lobe graph is drawn.
And step S7, performing milling stability prediction on the series-parallel machine tool system according to the stability lobe graph.
It should be noted that, in the present invention, the admittance coupling method, the fully discrete time domain method, and the florkey theory are all basic theories in the field of machine tool stability prediction, and are not described in detail herein.
In step S2, the frequency response functions of the first substructure 1 and the second substructure 2 can be obtained by the same method. Preferably, the frequency response functions of the first substructure 1 and the second substructure 2 in the free state are respectively measured by a hammering method. The hammering method measuring device comprises: a force hammer, a signal acquisition device (e.g., a high-precision acquisition instrument), an acceleration sensor, and a terminal device (e.g., a notebook computer, a desktop computer, etc.). The frequency response function is measured by:
arranging an acceleration sensor at a position to be measured, wherein the position to be measured refers to the position of a tool tip of the first substructure 1 to be measured or the position of a movable platform in the second substructure 2;
knocking at the position to be detected by adopting a force hammer, and obtaining acceleration information of the position to be detected by a signal acquisition device;
and processing the acceleration information and converting the acceleration information in a frequency domain by using Fourier transform to obtain a frequency response function of the position to be measured.
It should be noted that, when the frequency response functions of the first substructure 1 and the second substructure 2 in the free state are measured by using the hammering method, the first substructure 1 and the second substructure 2 are respectively regarded as a whole and measured.
When the low-order dynamic characteristics of the parallel/parallel-series mechanism are considered in the milling stability prediction, it is necessary to obtain the nose point frequency response function in the structure including the parallel/parallel-series mechanism, and therefore, after the frequency response functions of the first substructure 1 and the second substructure 2 are measured, it is necessary to obtain the dynamic characteristics of the joint surface. In an embodiment of the present invention, in the step of obtaining the nose point frequency response function by using the admittance coupling method, the dynamic characteristics of the junction surface of the first substructure 1 and the second substructure 2 are inversely obtained by the admittance coupling method.
In an embodiment of the present invention, in the step of determining the eigenvalue of the state transition matrix to obtain the stable state of the hybrid machine tool system, if the moduli of all eigenvalues of the state transition matrix are less than 1, the hybrid machine tool system is determined as a stable system, otherwise, the hybrid machine tool system is determined as an unstable system.
In one embodiment of the present invention, a milling kinetic equation under a modal coordinate system is solved by using a full discrete time domain method, and the step of obtaining a state transition matrix includes:
acquiring a low-order modal parameter and a high-order modal parameter by a modal parameter identification method;
and acquiring a state transition matrix according to the low-order modal parameters and the high-order modal parameters.
The mode refers to the natural vibration characteristic of the hybrid machine tool system, the mode parameters include frequency, damping ratio and mode shape, and each mode has specific natural frequency, damping ratio and mode shape. The modal parameter identification method may be an admittance circle identification method, an orthogonal polynomial curve fitting method, an analytical component method, and the like.
In the present application, the low-order modal parameter and the high-order modal parameter are not particularly limited to be divided.
The following describes the present embodiment by taking a milling workpiece as a rigid body, a hybrid machine tool system as a flexible body, and taking the motion trajectory of the cutter teeth during milling as an approximate circular arc trajectory.
When the motion track of the cutter teeth in the milling process is approximately regarded as an arc track, simplifying the cut thickness model to obtain a simplified cut thickness expression as shown in the following formula (1):
ul(t)＝ftsin(wl(t))+[x(t)-x(t-Tc)]sin(wl(t))-[y(t)-y(t-Tc)]cos(wl(t))(1)
wherein u isl(t) represents the cutting thickness of the 1 st tooth at time t, ftRepresenting feed per tooth, wl(T) represents the angle of rotation of the 1 st tooth at time T, TcRepresents the tooth passing frequency, t represents the time, x (t) represents the x-direction displacement of the tool center point at the time t, and y (t) represents the y-direction displacement of the tool center point at the time t.
Further, the milling force in the milling process is solved according to a simplified cutting thickness expression, and the milling cutting force is obtained as shown in the following formula:
wherein, Fx(t) x-direction milling cutting force, Fy(t) represents a milling cutting force in the y-direction, apThe axial cutting depth is indicated as the axial depth,
a matrix of force coefficients is represented by a matrix of force coefficients,
representing the static force matrix, T representing the time, TcRepresenting the tooth passing frequency, x1(t) x-direction displacement of the center point of the tool at time t, y1(t) denotes the displacement of the tool centre point in the y-direction at time t, the indices p, q, c themselves having no particular physical significance.
The tool 13-tool handle 12-main shaft 11-parallel/parallel-parallel mechanism system is regarded as a flexible body, vibration of the tool 13-tool handle 12-main shaft 11-parallel/parallel-parallel mechanism system in the x and y directions is considered, and a milling dynamic model with multiple degrees of freedom in two orthogonal directions is established based on a simplified thickness cutting model.
Assuming that the tool 13-tool shank 12-main shaft 11-parallel/parallel-parallel mechanism system has r-order modes in two directions respectively,
x(t)＝[x1x2… xi… xr]T(3)
y(t)＝[y1y2… yi… yr]T(4)
wherein x isiRepresenting the ith modal displacement in the x direction, r representing the modal order, yiRepresenting the ith modal displacement in the y-direction.
Obtaining a milling system kinetic equation under physical coordinates:
wherein the content of the first and second substances,
a quality matrix representing the series-parallel machine tool system,
a damping matrix representing the series-parallel machine tool system,
representing the stiffness matrix of the series-parallel machine tool system, Fx(t) represents a cutting force vector in the x-direction, Fy(t) represents a cutting force vector in the y direction, t represents time, x (t) represents x-direction displacement, and y (t) represents y-direction displacement.
Since the milling forces act only at the tool end points, the milling forces act only at the tool end points
Fx(t)＝[Fx(t) 0 … 0]T(6)
Fy(t)＝[Fy(t) 0 … 0]T(7)
Wherein the content of the first and second substances,Fx(t) represents milling force in x-direction, Fx(t) represents the milling force vector in the x-direction, Fy(t) represents the milling force in the y-direction, Fy(t) represents the y-direction milling force vector.
Converting the mass matrix, the damping matrix, the stiffness matrix and the cutting force vector under the physical coordinate system into a modal coordinate system, and converting the milling kinetic equation under the physical coordinate system into a milling kinetic equation under the modal coordinate system, as shown in the following formula (8):
wherein M represents a mass matrix of the series-parallel machine tool system, C represents a damping matrix of the series-parallel machine tool system, K represents a stiffness matrix of the series-parallel machine tool system, q (t) represents displacement under a modal coordinate system of the system,
representing the velocity in the modal coordinate system,
represents the acceleration in the modal coordinate system, apIndicating axial depth of cut, Kq(t) represents a force coefficient matrix, fq(T) denotes the static force matrix, the indices c, p, q have no particular meaning, TcRepresenting the tooth pass frequency. Wherein q (t) ═ qx(t) qy(t)]T，qx(t) represents the modal displacement of the system in the x-direction, qx(t) represents modal displacement in the y-direction of the system.
Solving a milling kinetic equation by using a full discrete time domain method to obtain a state transition matrix phi of the system, which is shown in the following formula (9):
Φ＝Dm-1Dm-2…D1D0
where Φ represents a state transition matrix and D represents an intermediate variable matrix calculated using a full discrete time domain method.
Wherein the intermediate variable D is obtained by the following formula (10):
wherein, the matrix DkThe parameters in (1) are intermediate variables calculated by using a full discrete time domain method, and have no physical significance.
The state transfer matrix phi acquires modal parameters through a modal parameter identification method, low-order modal parameters and high-order modal parameters are obtained by substituting in a formula (9), and the characteristic value of the state transfer matrix phi is judged according to the Floquest theory to obtain the stable state of the hybrid machine tool system, including stability and instability, so that a stable lobe graph considering the low-frequency dynamic characteristic of the parallel/parallel hybrid mechanism is drawn.
Milling stability experiment verification is carried out on the method for predicting the milling stability of the hybrid machine tool, the experiment platform is the hybrid machine tool based on a 3-P (4R) S mechanism, the used electric spindle is an air-cooled electric spindle of Omlat company of Italy, the model of a tool holder interface is HSK63A, full-cutter slot milling experiment is carried out, the cutting material is aviation aluminum alloy 7075T7451, and the cutting mode is forward milling. The machine tool posture is (0 degree ), the feeding amount of each tooth is set to be 0.02mm, the range of the main shaft rotating speed is 2000 plus 9000rpm, and one rotating speed (8 groups in total) is selected every 1000 rpm. At each rotating speed, the axial cutting depth is gradually increased from 1mm, and is increased by 1mm each time until the phenomenon that the machine tool vibrates is monitored.
Fig. 3 is a verification result diagram of the milling stability prediction method of the present invention, and fig. 3 shows verification comparison of the stability lobe diagram considering the low-frequency dynamic characteristic of the parallel/parallel hybrid mechanism and the stability lobe diagram considering the structural dynamic characteristic of the parallel mechanism with respect to the milling stability prediction result. As shown in fig. 3, a in the graph represents a stable point, B represents an unstable point, and a stable lobe graph is drawn according to a boundary between the stable point and the unstable point, and the result shows that a prediction result obtained by using the milling stability prediction method of the hybrid machine tool is completely consistent with an experimental result, which proves that the accuracy of the stable lobe graph considering the low-frequency dynamic characteristic of the structure is higher. Compared with the method only considering the medium-high frequency dynamic characteristic, the method comprehensively considers the influence of the low-order dynamic characteristic and the medium-high order dynamic characteristic of the parallel mechanism on the milling stable region low rotating speed section, and greatly improves the prediction accuracy of the milling stability of the series-parallel machine tool.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A method for predicting milling stability of a series-parallel machine tool is characterized by comprising the following steps:
the method comprises the following steps of dividing the whole series-parallel machine tool system into a cutter, a cutter handle, a main shaft and a parallel/parallel series-parallel mechanism, wherein the cutter, the cutter handle and the main shaft are used as a first substructure, and the parallel/parallel series-parallel mechanism is used as a second substructure;
measuring and obtaining frequency response functions of the first substructure and the second substructure, and obtaining a tool nose point frequency response function by using an admittance coupling method;
establishing a milling kinetic equation under a physical coordinate system with multiple degrees of freedom in two orthogonal directions by taking a milling workpiece as a rigid body and a parallel-series machine tool system as a flexible body;
converting a milling kinetic equation under a physical coordinate system into a milling kinetic equation under a modal coordinate system;
solving a milling kinetic equation under a modal coordinate system by adopting a full discrete time domain method to obtain a state transition matrix;
judging the characteristic value of a state transition matrix according to a Frokay theory to obtain the stable state of the series-parallel machine tool system, and drawing a stability lobe graph;
and carrying out milling stability prediction on the hybrid machine tool system according to the stability lobe graph.
2. The method for predicting milling stability of a hybrid machine tool according to claim 1, wherein the milling kinetic equation in the physical coordinate system is as follows:
wherein the content of the first and second substances,
a quality matrix representing the series-parallel machine tool system,
a damping matrix representing the series-parallel machine tool system,
representing the stiffness matrix of the series-parallel machine tool system, Fx(t) represents a cutting force vector in the x-direction, Fy(t) represents a cutting force vector in the y direction, t represents time, x (t) represents displacement in the x direction, and y (t) represents displacement in the y direction.
3. The method for predicting milling stability of a hybrid machine tool according to claim 2, wherein the milling kinetic equation in the modal coordinate system is shown as follows:
wherein M represents a mass matrix of the series-parallel machine tool system, C represents a damping matrix of the series-parallel machine tool system, K represents a stiffness matrix of the series-parallel machine tool system, q (t) represents displacement in a modal coordinate system,
representing the velocity in the modal coordinate system,
represents the acceleration in the modal coordinate system, apIndicating axial depth of cut, Kq(t) represents moment of force coefficientArray, fq(T) represents the static force matrix, TcRepresenting the tooth pass frequency.
4. The milling stability prediction method of the hybrid machine tool according to claim 3, wherein the obtained state transition matrix Φ is represented by the following formula:
Φ＝Dm-1Dm-2…D1D0
where Φ represents a state transition matrix and D represents an intermediate variable matrix calculated using a full discrete time domain method.
5. The method for predicting milling stability of a hybrid machine tool according to claim 2, wherein in the step of establishing the milling kinetic equation under the physical coordinate system orthogonal to the two directions with multiple degrees of freedom, the milling cutting force is obtained by the following formula:
wherein, Fx(t) x-direction milling cutting force, Fy(t) represents a milling cutting force in the y-direction, apThe axial cutting depth is indicated as the axial depth,
a matrix of force coefficients is represented by a matrix of force coefficients,
representing the static force matrix, T representing the time, TcRepresenting the tooth passing frequency, x1(t) x-direction displacement of the center point of the tool at time t, y1(t) represents the y-direction displacement of the tool center point at time t.
6. The method for predicting milling stability of a hybrid machine tool according to claim 1, wherein in the step of obtaining the nose point frequency response function by using the admittance coupling method, the dynamic characteristics of the junction surfaces of the first substructure and the second substructure are reversely obtained by using the admittance coupling method.
7. The method for predicting milling stability of a hybrid machine tool according to claim 1, wherein the step of measuring and acquiring the frequency response functions of the first substructure and the second substructure comprises:
arranging an acceleration sensor at a position to be measured;
knocking at the position to be detected by adopting a force hammer, and obtaining acceleration information of the position to be detected by a signal acquisition device;
and processing the acceleration information and converting the acceleration information in a frequency domain by using Fourier transform to obtain a frequency response function of the position to be measured.
8. The method for predicting milling stability of a hybrid machine tool according to claim 1, wherein in the step of determining the eigenvalue of the state transition matrix to obtain the stable state of the hybrid machine tool system, if the moduli of all eigenvalues of the state transition matrix are less than 1, the hybrid machine tool system is determined as a stable system.
9. The milling stability prediction method of the hybrid machine tool according to claim 1, wherein the milling kinetic equation under the modal coordinate system is solved by a full discrete time domain method, and the step of obtaining the state transition matrix comprises:
acquiring a low-order modal parameter and a high-order modal parameter by a modal parameter identification method;
and acquiring a state transition matrix according to the low-order modal parameters and the high-order modal parameters.
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