CN114895565A - Milling working condition-oriented dynamic characteristic real-time prediction method for double-turntable five-axis machine tool - Google Patents

Abstract

The invention discloses a method for predicting dynamic characteristics of a double-turntable five-axis machine tool in real time under a milling working condition, and belongs to the technical field of machine tool manufacturing. The method comprises the following steps: describing a machine tool kinematic model by using a standard D-H method; establishing a machine tool kinetic equation by using a Lagrange method; establishing a dynamic model of a main shaft-tool handle, a main shaft-bearing, a guide rail sliding block and a ball screw joint part by adopting a Gicunx Kozaki integration method, a Hertz theory and elastic mechanics to obtain contact characteristic parameters of the joint part; and finally, establishing a kinetic model by combining a kinetic equation and the contact characteristics of the binding part. The dynamic characteristics of the machine tool are predicted in real time according to the milling working condition, the working position and the posture in the actual milling state of the machine tool, the problem that the dynamic characteristics of a static machine tool in the traditional method are different from those in the actual milling state is solved, the calculation efficiency is high, and the dynamic characteristics in the milling operation of the machine tool can be simulated, tracked and predicted by using a digital twin organism.

Description

Real-time prediction method of dynamic characteristics of double-turntable five-axis machine tool under milling conditions

technical field

The invention belongs to the technical field of machine tool manufacturing, and particularly relates to a dynamic characteristic prediction method of a double-turntable five-axis numerically controlled machine tool under milling conditions.

Background technique

Multi-axis CNC machine tools have a deep influence on high-end fields such as national military, aviation, aerospace, scientific research, precision instruments, and high-precision medical equipment. High-level CNC machine tools have the advantages of high speed, high precision, and good reliability. They are used in almost every branch of modern industry and are the starting point for most industrial manufacturing. In order to stabilize the machining process, improve the surface machining quality, and avoid the occurrence of chatter vibration and the deterioration of the workpiece surface during the machining process of the CNC machine tool, it is necessary to clarify the dynamic characteristics of the CNC machine tool and guide the optimization of the machining process. Therefore, the efficient and accurate simulation and prediction of the dynamic characteristics of CNC machine tools is of great significance to ensure the stability of the processing process and the quality of workpiece surface processing.

In the actual machining process of CNC machine tools, the operating conditions, machining position, attitude, contact between joints, friction and other factors of the machine tool are in the process of dynamic change. At this time, the dynamic characteristics of the machine tool also change dynamically, which is different from the static state. Therefore, considering factors such as milling conditions, processing position, attitude, contact between joints, friction, etc., to predict the dynamic characteristics of CNC machine tools efficiently and accurately, it is particularly important to guide process optimization and control workpiece surface quality.

At present, the commonly used dynamic modeling methods include lumped mass model, transfer matrix model, substructure model and finite element analysis model.

1. The lumped mass model method is to segment the research object and connect it through points with fixed mass constraints, each segment is regarded as a rigid body or elastic body without fixed mass constraints, so that the continuous system is transformed into a system with limited freedom, but the result is desired The number of more accurate concentrated masses will be very large, and the amount of calculation will become very large, and it is difficult to achieve the requirements of real-time prediction.

2. The transfer matrix model method is to regard the overall structure as a mechanical problem of connection and transfer of multiple substructures, establish a substructure transfer matrix, and analyze the entire structure through matrix multiplication. However, when solving the dynamic problems of large and complex rotor systems The problem of slow calculation speed and numerical instability due to the increase of trial calculation frequency.

3. The substructure model method is similar to the transfer matrix model method. The difference is that the dynamic characteristic parameters of each substructure are obtained through theoretical research, practical experiments and numerical calculations, and then the dynamic models of each substructure are integrated to obtain The dynamic characteristics of the overall structure, this method is more suitable for studying a certain structure in a complex system, and the modeling steps for the whole system are complicated and the accuracy is low.

4. The finite element model method regards the complete structure as a plurality of elements connected at the node position, and the connected node displacement is expressed as an unknown parameter with the relevant displacement function, and then the vibration balance equation of the overall structure is obtained through the energy variation principle. The solution accuracy is high and the relevant commercial software is mature, but only one dynamic model can be established in a single processing. When the working position, attitude and milling conditions are changed, the model needs to be re-established to solve, which is not suitable for the dynamic characteristics of the machine tool under the milling conditions. Real-time tracking simulation, and the calculation speed is low and time-consuming, resulting in low modeling and analysis efficiency.

The dynamic characteristics of the machine tool change with the transformation of milling conditions and poses in the actual milling state, so it is difficult for the existing dynamic modeling methods to achieve a high degree of pose transformation in the entire working space of the machine tool under different milling conditions. Efficiency forecast. Moreover, the current research on the dynamic characteristics of the machine tool is to apply excitation to the machine tool bed in a static state to obtain the response signal, and to obtain the modal parameters of the machine tool by processing the response signal, which is very different from the actual operating conditions and is not close to reality. Happening.

SUMMARY OF THE INVENTION

The invention considers the milling working condition, processing position, attitude and contact characteristics of the joint part, establishes a dynamic model of a double turntable five-axis machine tool with low degrees of freedom, and predicts the dynamic characteristics of the machine tool in real time according to the Jacobian matrix of the transformed position and different milling working conditions of the machine tool , which is closer to the actual milling state and has high computational efficiency. At the same time, it can be used as a digital twin to simulate, track and predict the dynamic characteristics of machine tool milling operations. It can solve the problem that traditional methods ignore the actual operation of the machine tool when studying the dynamic characteristics of the machine tool in a static state. However, the calculation speed of the dynamic model is low and it is not real-time, and it is difficult to analyze the pose transformation in the entire working space of the machine tool.

The object of the present invention is to provide a real-time prediction method for the dynamic characteristics of a dual-turntable five-axis CNC machine tool under milling conditions, the method comprising:

Step 1: Establish the kinematic chain of the double-turntable five-axis CNC machine tool according to the machine tool structure and motion state, use the standard D-H method to establish a parameter model, and describe the complete kinematics model of the double-turntable five-axis CNC machine tool through the homogeneous coordinate transformation between the coordinate systems. ;

Step 2: Establish a three-dimensional solid model of the dual-turntable five-axis CNC machine tool, and use the three-dimensional solid model to obtain the mass of each component of the dual-turntable five-axis CNC machine tool, its own center of mass, and the inertia tensor at the center of mass, and obtain the complete double-turntable five-axis CNC machine tool. The kinetic energy and potential energy expressions of the system are derived, and the dynamic equation of the double-turntable five-axis CNC machine tool is derived by using the Lagrangian method;

Step 3: Use Yoshimura's integration method, Hertz contact theory and elastic mechanics to establish the dynamic models of the spindle-tool shank joint, spindle-bearing joint, guide-slider joint and ball screw joint under milling conditions , to obtain the contact characteristic parameters of the spindle-tool shank joint, the spindle-bearing joint, the guide-slider joint and the ball screw joint under milling conditions;

Step 4: Establish a complete multi-body dynamics model of the dual-turntable five-axis CNC machine tool combined with the dynamic equation of the dual-turntable five-axis CNC machine tool and the contact characteristic parameters of the joint, and solve the model.

The present invention proposes a real-time prediction method for the dynamic characteristics of a dual-turntable five-axis numerically controlled machine tool under milling conditions, and the beneficial effects that can be achieved are as follows:

1. The present invention can perform real-time prediction of the dynamics of a dual-turntable five-axis CNC machine tool under milling conditions, and predict dynamic characteristics for different milling conditions, different processing positions and attitudes, compared to ignoring milling conditions and processing positions. With the existing methods of attitude change, the prediction results are closer to the actual motion state of the machine tool and more accurate, so as to analyze and evaluate the dynamic characteristics of the machine tool, which is used to guide the optimization of the milling process, improve the milling processing efficiency and the surface quality of the machined workpiece.

2. The dynamic model established by the present invention takes into account the actual milling conditions of the machine tool, and only needs to change the position Jacobian matrix parameters to transform the machine tool pose, and it is no longer necessary to repeat the modeling of the machine tool under specific conditions, which solves the problem. The inefficiency of working pose transformation for dynamic analysis of five-axis CNC machine tools with double turntables.

3. The present invention obtains the characteristic parameters of each structural component (mass, its own center of mass, inertia tensor at the center of mass) by establishing a three-dimensional model of a five-axis CNC machine tool with a double turntable, and at the same time establishes each joint of the machine tool (spindle-tool holder joint). , the spindle-bearing joint, the guide-slider joint and the ball screw joint) contact model to obtain the contact characteristic parameters of the joint, especially considering the influence of milling load, centrifugal force and gyro moment during the milling process, comprehensive machine tool structural parts The overall dynamic model is established with the joint part, and the dynamic characteristics of the dual-turntable five-axis CNC machine tool obtained from this are more in line with the actual situation, with higher accuracy, and meet the accuracy requirements of machine tool dynamics modeling and analysis.

4. The present invention has high calculation efficiency for establishing a dynamic model, meets the requirements of high efficiency and real-time performance of modeling and analysis, and can be used as a digital twin to simulate the machine tool in milling operation to track and predict dynamic characteristics.

Description of drawings

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

Fig. 1 is the structural analysis diagram of the double-turntable five-axis CNC machine tool of the present invention;

Fig. 2 is the force analysis diagram of the spindle system of the dual-turntable five-axis CNC machine tool according to the present invention;

Fig. 3 is the mechanical model diagram of the guide rail joint of the dual-turntable five-axis CNC machine tool under the milling load according to the present invention;

Fig. 4 is the force analysis diagram of the simplified model of the rolling linear guide rail of the double turntable five-axis CNC machine tool according to the present invention;

5 is a schematic diagram of the geometric relationship of the rolling elements of the ball screw motion pair of the double turntable five-axis CNC machine tool according to the present invention;

FIG. 6 is a schematic diagram of a dynamic model analysis result of the dual-turntable five-axis CNC machine tool according to the present invention;

Fig. 7 is the frequency response function curve of the dual-turntable five-axis CNC machine tool under different attitudes;

Fig. 8 is the frequency response function curve under different milling loads of the dual-turntable five-axis CNC machine tool according to the present invention;

FIG. 9 is a specific flow chart of the method for real-time prediction of multi-body dynamics characteristics of a dual-turntable five-axis CNC machine tool according to the present invention.

In the figure: 1. Machine tool frame; 2. X-axis guide rail; 3. Y-axis guide rail; 4. A-axis swing table; 5. C-axis table; 6. Z-axis guide rail; 7. Spindle tool;

Detailed ways

The specific steps of the method embodiment of the present invention will be clearly and completely described below with reference to the accompanying drawings in the method embodiment of the present invention.

S1: Taking the double-turntable five-axis CNC machine tool as an example, the kinematic chain model of the double-turntable five-axis CNC machine tool is established according to the overall structure of the double-turntable five-axis CNC machine tool and the kinematic relationship between the sub-structures, as shown in Figure 1. The standard D-H parameter method is used to describe the coordinate system transformation between the seven substructures of the dual-turntable five-axis CNC machine tool, and the complete kinematics model of the dual-turntable five-axis CNC machine tool is established; the details include:

S11: Double turntable five-axis CNC machine tool has five linkage axes, including X-axis guide 2, Y-axis guide 3, Z-axis guide 6, A-axis swing table 4, and C-axis table 5. X-axis guide 2: The slide rail moves back and forth; Y-axis guide 3: The slide rail moves with the worktable left and right; Z-axis guide 6: The slide rail moves up and down perpendicular to the ground; A-axis swing table 4: The worktable swings around the Y-axis; C Axis table 5: The table rotates 360° around the Z axis.

The tool is fixed on the Z axis and is connected to the part of the machine frame perpendicular to the ground through the slide rail, the part of the machine frame parallel to the ground is connected to the X-axis guide rail 2, the X-axis guide rail 2 is connected to the Y-axis guide rail 3, and the Y-axis guide rail 3 passes through The A-axis swing table 4 is connected to the C-axis table 5 . When the machine tool is working, the workpiece is fixed on the C-axis table 5, and the position of the workpiece and the tool are adjusted by the rotation of the C-axis table 5, the swing of the A-axis table 4, the translation of the Y-axis guide 3 and the translation of the X-axis guide 2. The Z-axis guide 6 moves up and down to process the workpiece. Therefore, the kinematic chain relationship of the dual-turntable five-axis CNC machine tool of the present invention is: C-axis table 5→A-axis swing table 4→Y-axis guide rail 3→X-axis guide rail 2→machine frame 1→Z-axis guide rail 6.

S12: When using the standard DH parameter method to describe the coordinate system transformation between the sub-structures of the double-turntable five-axis CNC machine tool, four parameters a _i , α _i , d _i and θ _i are used, where a _i refers to the structure is the common normal distance between the two axes of the component, α _i refers to the angle between the two axes of the structural component perpendicular to the plane where a _i is located, d _i represents the distance between adjacent structural components, θ _i represents the rotation angle between adjacent structural components, Therefore, the relationship between two adjacent structural members is the homogeneous coordinate transformation from the coordinate system {x ₁ , y ₁ , z ₁ } to the coordinate system {x ₀ , y ₀ , z ₀ }. According to the standard DH method, adjacent two The coordinate transformation relationship between the structural parts is:

表示坐标系{i}相对于坐标系{i-1}的位置和方向，

表示沿Z_i-1轴移动d_i，

表示沿Z_i-1轴转动θ_i，

表示沿X_i轴移动a_i，

表示沿X_i轴转动α_i。in

represents the position and orientation of coordinate system {i} relative to coordinate system {i-1},

represents the movement of d _i along the Z _i-1 axis,

represents the rotation θ _i along the Z _i-1 axis,

represents moving a _i along the X _i axis,

represents the rotation of α _i along the X _i axis.

The DH parameter table of the double turntable five-axis CNC machine tool is shown in Table 1. q ₁ represents the X axis of the machine tool movement axis, q ₂ represents the machine tool movement axis Y axis, q ₃ represents the machine tool movement axis Z axis, and q ₄ represents the machine tool swing axis A Axis, q ₅ represents the C axis of the machine tool rotation axis, that is, the worktable.

Table 1 Standard D-H parameters of double turntable five-axis CNC machine tools

来表示：S13: Establish the machine tool coordinate system, take the bottom center of the bed as the origin O, establish the bed coordinate system OBED, the X axis corresponds to the coordinate system OSX, the Y axis corresponds to the coordinate system OSY, the A axis corresponds to the coordinate system OSA, the worktable coordinate system OST, The Z axis corresponds to the coordinate system OSZ, and the tool point coordinate system OTCP. By analyzing the transformation relationship of the kinematic chain from the worktable to the tool of the double-turntable five-axis CNC machine tool, it is found that six coordinate transformations are required to convert from the worktable coordinate system to the tool coordinate system, namely OST→OSA→OSY→OSX→OBED→OSZ →OTCP, so the overall complete kinematic model of the double turntable five-axis CNC machine tool uses the total coordinate transformation matrix

To represent:

表示结构件的旋转矩阵，p＝[p_x p_y p_z]^T表示结构件的位移矩阵。in

represents the rotation matrix of the structural part, and p=[p _x p _y p _z ] ^T represents the displacement matrix of the structural part.

S2: Establish a solid model of the double-turntable five-axis CNC machine tool, obtain the mass of each component, the coordinates of the center of mass, and the inertia tensor at the center of mass, and obtain the kinetic energy and potential energy expressions of the double-turntable five-axis CNC machine tool system. The dynamic equation of the double-turntable five-axis CNC machine tool is derived by the Grange method; the details include:

S21: Establish a three-dimensional solid model of the double-turntable five-axis CNC machine tool by referring to the machine tool manual, and use the three-dimensional model to obtain the mass mi, center of mass coordinates _Gi and inertia tensor _{I i} at the center of mass _Gi of each component.

S22: The translation speed v _i and rotation speed w _i of all components in the same coordinate system of each structural component of the double-turntable five-axis CNC machine tool are calculated by the time differential of the homogeneous transformation matrix, that is, converted into the corresponding Jacobian matrix form:

The system kinetic energy of the double turntable five-axis CNC machine tool is divided into two parts, one part is the kinetic energy E _l of the structural parts, and the other part is the kinetic energy E _r of the motor-driven rotor. Suppose the kinetic energy of the i-th structural member relative to the inertial coordinate system is E _li , and the kinetic energy of the differential mass dm on the structural member is recorded as dE _li , then:

Let I _i be the inertia tensor matrix of structural member i:

The mass of the structural part is m _i , and the inertia tensor matrix is I _i , then the kinetic energy of the structural part of the double turntable five-axis CNC machine tool is:

Denote the driving rotor of the motor on the i-th structural member as I _zi , then the sum of the rotational kinetic energy of the n rotors of the double turntable five-axis CNC machine tool is:

To sum up, it can be concluded that the overall kinetic energy of the dual-turntable five-axis CNC machine tool is the sum of the kinetic energy of the drive shaft rotor and the kinetic energy of the structural parts:

S23: The only source of potential energy of the double turntable five-axis CNC machine tool is gravity, and the mass of the object is concentrated at the center of mass, so the potential energy of the i-th structural member is:

P _i =m _i gC _i (9)

where g is the gravity vector in the inertial coordinate system, and C _i is the center of mass coordinate of the structural member i. Then the total potential energy of the double turntable five-axis CNC machine tool is:

S24: The Lagrange function L is recorded as the difference between the kinetic energy and the potential energy of the double turntable five-axis CNC machine tool:

L=E _k -E _p (11)

By derivation of the above formula, the Lagrange equation of the dynamics of the dual-turntable five-axis CNC machine tool can be obtained:

Substitute the kinetic energy and potential energy into the Lagrange function constructed by (12), we can get:

Substitute equations (8) and (10) into the above equations, we can get:

The above formula is simplified to:

为离心力和科氏力矢量，G(q)为结构件重力矢量矩阵，F为切削过程中产生的摩擦力和切削力构成的应用力向量，M(q)、

分别用相关雅可比矩阵表示为：where M(q) is the mass matrix of each structural member,

are centrifugal force and Coriolis force vector, G(q) is the gravity vector matrix of the structural part, F is the applied force vector formed by the friction force and cutting force generated in the cutting process, M(q),

They are represented by the relevant Jacobian matrix as:

S3: The rigidity model of the spindle-tool shank joint is established by the Yoshimura integration method, and the dynamic models of the spindle-bearing joint, the guide-slider joint and the ball screw joint are obtained by using the Hertz contact theory and the principle of mechanical balance. Simultaneously establish the contact characteristic parameters of each joint of the dual-turntable five-axis CNC machine tool under the milling condition; the details include:

S31: Perform force analysis on the spindle system in the milling state. As shown in Figure 2, the spindle-tool shank joint is affected by the milling loads F _x , F _y , F _z and centrifugal force, and the average normal direction of the spindle-tool shank joint is The force P _n1 is:

Among them, F ₀ is the clamping force of the spindle-tool holder, F _n1 is the normal force of the spindle-tool holder joint, S ₁ is the contact area of the spindle-tool holder, φ ₁ is the included angle of the tool holder, and L ₁ is the spindle- The axial length of the shank joint, r ₁ and r ₂ are the large and small radii of the joint, and μ ₁ is the friction coefficient.

The equivalent spring stiffness of the spindle-tool shank joint is obtained by Yoshimura's integration method:

作用下结合部内部件变形最大量，

E为弹性模量，υ为泊松比，R为结合部半径，δ_j为离心力引起结合部径向间隙，当主轴转速为n，则离心力为

b为主轴外径。where k(δ) can be obtained by transforming the integral curve of Yoshimura Yutaka, α ₀ and β ₀ are the contact characteristic parameters of the joint, and δ _rm is the radial milling load

The maximum amount of deformation of the internal parts of the joint under the action,

E is the elastic modulus, υ is the Poisson’s ratio, R is the radius of the joint, δ _j is the radial gap of the joint caused by centrifugal force, and when the spindle speed is n, the centrifugal force is

b is the outer diameter of the main shaft.

S32: In the milling state, the spindle-bearing joint is affected by the milling loads F _x , F _y , F _z , centrifugal force and gyro moment, as shown in Figure 3, according to the Hertz theory, the force balance equation of the t-th rolling element of the bearing for:

Among them, Q _it and Q _ot are the contact loads between the rolling element and the inner and outer rings, α _it and α _ot are the contact angles of the rolling element and the inner and outer rings, M _gt is the gyro moment, F _ct is the centrifugal force, and D is the diameter of the rolling element.

Perform an overall force analysis on the bearing:

后主轴-轴承结合部受到的径向载荷

γ_t第t个滚动体为方位角，z为轴承中滚动体的数目。where _Ri is the radius of the inner raceway curvature center circle, ri is the radius of the inner raceway, F _rx is the radial load _on the front and rear spindle-bearing joints, and the radial load on the front spindle-bearing joint

Radial load on the rear spindle-bearing joint

γ _t The t-th rolling element is the azimuth angle, and z is the number of rolling elements in the bearing.

The Newton-Raphson iteration method is used to solve the equation system, and the force balance formula of the bearing inner ring with different degrees of freedom is obtained through coordinate transformation, and the contact force between all the rolling elements and the inner and outer rings is accumulated, and the resultant force is derived from the displacement, and the spindle-bearing joint is obtained. Contact stiffness matrix.

S33: In the milling state, the joint of the rolling linear guide is affected by the milling loads F _x , F _y , and F _z . Taking the joint of the Z-axis guide as an example, a mechanical model under the milling load is established, as shown in Figure 3, the mechanical balance equation is expressed as follows:

Among them, M _x , My _y and M _z are the three-way torques of x, y and z, respectively, P _x and P _y are the overall component forces acting on the x and y directions of the guide rail pair, and F _qz is the ball screw pair. Traction force, G ₁ is the weight of the tool holder, and G ₂ is the overall weight of the guide rail pair.

Since the z direction is the direction of slider motion, there is no fixed constraint, so there is no reaction force. The joint part between the guide rail and the slider is divided into four areas, and the decomposition load generated when each reaction force and reaction moment acts alone is evenly distributed to the joint part between the slider and the guide rail. Normal force and tangential force of each joint:

Among them, i, j=1, 2 represent the number of each joint respectively, P _xij (n), P _yij (n) are each reaction force or moment acting alone to generate component force at the joint.

Since the size and number of balls in the guide rail are the same, the guide rail, slider, and ball can be simplified accordingly to solve the elastic deformation between the joints under load, as shown in Figure 4.

Only considering the normal force acting on the guide rail, the force analysis of the rolling linear guide is carried out:

(F ₁ -F ₃ )nsinγ=F _y /2 (24)

According to the superposition theory of mechanics:

Among them, n is the number of balls in a single-row track, F _P is the normal component force of the preload acting on the ball, and γ is the angle formed by the contact between the ball and the raceway.

According to the Hertz contact theory, the contact changes between the ball and the slider, and between the ball and the guide rail are:

where E ₁ , E ₂ , E ₃ and μ ₁ , μ ₂ , μ ₃ represent the elastic modulus and Poisson’s ratio of the ball, slider and rolling linear guide materials, respectively, ∑ρ is the sum of the principal curvatures at the internal contact points, ∑ ρ=ρ ₁ +ρ ₂ +ρ ₃ +ρ ₄ , and ρ ₁ =ρ ₂ =2/d _b , ρ ₃ =−f/d _b ,ρ ₄ =0, _db is the ball diameter, and f is the raceway The ratio of the radius of curvature to the diameter of the ball, the value of J/m _a can be obtained by looking up the table by calculating the value of τ, and τ=|ρ ₃ -ρ ₄ |/∑ρ.

Then the normal and tangential contact stiffnesses of the rail joint are:

Where α is the angle between the normal force of the rolling element and the longitudinal axis.

S34: Take the Z-axis ball screw joint as an example, and establish a mechanical model of the joint in the milling state. Figure 5 shows the geometric relationship between the contact deformation of the rolling element and the screw raceway, and the left side represents the rolling element and the screw raceway. Side geometric relationship, the right side represents the geometric relationship between the rolling element and the lower side of the screw raceway, we can get:

When the rolling element is in contact with the upper side of the screw raceway, take +δ _tz , when the rolling element is in contact with the lower side of the screw raceway, take -δ _tz , α ₀ , α _t are the contact angle before deformation and The contact angle after deformation, A ₀ is the center distance between the center of curvature of the screw raceway and the center of the nut raceway curvature, V _tz , V _ty are the axial and radial distances of the center of curvature of the screw raceway after contact deformation, respectively , δ _tz , δ _ty are the axial displacement and radial displacement of the screw raceway curvature center, respectively.

Further analysis obtains the displacement balance equation:

For the force analysis of the rolling elements of the ball screw motion pair, the force balance equation of the rolling elements is:

为第t个滚动体方位角，ψ丝杠滚道螺旋角。where Q _t is the contact load of the rolling element, f _tx , f _ty , and f _tz are the force on the kth rolling element,

is the azimuth angle of the t-th rolling element, and ψ is the helix angle of the screw raceway.

Under the action of the milling load, the force analysis between the rolling elements and the screw raceway in the ball screw kinematic pair is carried out, and the mechanical balance equation between all the rolling elements and the screw raceway is established as follows:

Through the force balance formula of each rolling element, the contact force of all rolling elements is accumulated, and the resultant force is derived from the displacement, and the contact stiffness matrix of the joint part of the ball screw kinematic pair in the milling state is obtained.

S4: Finally, a complete multi-body dynamic model of the dual-turntable five-axis CNC machine tool is established by combining the dynamic equations of the dual-turntable five-axis CNC machine tool and the contact characteristic parameters of the main joints, which is represented by the following differential equation:

Among them, K(q) is the contact stiffness matrix of the main joint. Combined with the contact characteristic parameters of each component of the double-turntable five-axis machine tool and the joint surface, the dynamic equation of the whole machine of the double-turntable five-axis CNC machine tool under the milling condition is analyzed and solved. Simulation calculation, the frequency response function curve obtained by calculation and analysis is shown in Figure 6, wherein the solid line represents the frequency response function curve obtained by actual experimental calculation, and the dotted line represents the frequency response function curve calculated by the dynamic model established by the present invention, From this, it can be seen that the model established by the present invention is accurate, the accuracy of the dynamic model is improved, and it is closer to the dynamic characteristics of the machine tool under actual operating conditions; the present invention can predict the machine tool in real time by changing the position Jacobian matrix and the milling load. Dynamic characteristics, Figure 7 shows the frequency response function curve of the double-turntable five-axis machine tool when the machining position changes, Figure 8 shows the frequency response function curve of the double-turntable five-axis machine tool when the milling load changes, and uses computer language to analyze all the dynamic model. The time required for modal parameters is less than 0.1ms, the calculation efficiency is high, and it meets the requirements of real-time prediction; the specific process of the implementation of the method of the present invention is shown in Figure 9, which can obtain different poses and different millings of a double-turntable five-axis CNC machine tool The natural frequency and frequency response function under load are convenient for efficient analysis of machine tool pose transformation under milling conditions.

The real-time prediction method of the dynamic characteristics of the double-turntable five-axis machine tool under the milling condition provided by the present invention has been described in detail above. In this paper, the double-turntable five-axis CNC machine tool is used to illustrate the principle and implementation of the present invention. The above implementation The description of the example is only used to help understand the method of the present invention and its core idea; meanwhile, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific embodiment and the scope of application. As stated, the contents of this specification should not be construed as limiting the present invention.

Claims (2)

1. a real-time prediction method for the dynamic characteristics of a double-turntable five-axis machine tool under milling conditions, is characterized in that, the method comprises the following steps: S1: analyze the structure and motion state of a double-turntable five-axis CNC machine tool, and establish a double-turntable five-axis CNC machine tool. The kinematic chain of the 5-axis CNC machine tool is established; the standard D-H parameter table of the dual-turntable five-axis CNC machine tool is established; the standard D-H method is used to describe the coordinate system transformation relationship between the sub-structures, and the complete kinematic model of the dual-turntable five-axis CNC machine tool is described; S2: Establish a three-dimensional solid model of the double-turntable five-axis CNC machine tool, and use the three-dimensional solid model to obtain the mass of each component, the coordinates of the center of mass, and the inertia tensor at the center of mass; obtain the kinetic energy and potential energy expression of the double-turntable five-axis CNC machine tool system. formula, using the Lagrangian method to deduce the dynamic equation of the double-turntable five-axis CNC machine tool; S3: The dynamic model of the spindle-tool shank joint, the spindle-bearing joint, the guide-slider joint and the ball screw joint under milling conditions is established by using the Yoshimura Yuntaka integral method, Hertz contact theory and elastic mechanics. Obtain the contact characteristic parameters of the spindle-tool shank joint, the spindle-bearing joint, the guide-slider joint and the ball screw joint under milling conditions; S4: Finally, a complete multi-body dynamic model of the dual-turntable five-axis CNC machine tool is established by combining the dynamic equations of the dual-turntable five-axis CNC machine tool and the contact characteristic parameters of the joint, and the model is solved; 2. according to a kind of real-time prediction method for the dynamic characteristics of double turntable five-axis numerically controlled machine tools described in claim 1, it is characterized in that, described step S1 specifically comprises: S11: Establish the machine tool kinematic chain of the double turntable five-axis CNC machine tool: C-axis table → A-axis swing table → Y-axis slide rail → X-axis slide rail → machine bed → Z-axis slide rail; S12: Use the standard DH parameter method to establish a parameter table of a five-axis CNC machine tool with a double turntable, and use four parameters, a _i , α _i , d _i and θ _i to describe the coordinate system transformation relationship between adjacent structural parts:

in

represents the position and orientation of coordinate system {i} relative to coordinate system {i-1},

represents the movement of d _i along the Z _i-1 axis,

represents the rotation θ _i along the Z _i-1 axis,

represents moving a _i along the X _i axis,

represents the rotation of α _i along the X _i axis; S13: Establish the machine tool coordinate system, take the bottom center of the bed as the origin O, establish the bed coordinate system OBED, the X axis corresponds to the coordinate system OSX, the Y axis corresponds to the coordinate system OSY, the A axis corresponds to the coordinate system OSA, the worktable coordinate system OST, The Z axis corresponds to the coordinate system OSZ, the tool position point coordinate system OTCP, and the transformation from the table coordinate system to the tool coordinate system needs to undergo six coordinate transformations, namely OST→OSA→OSY→OSX→OBED→OSZ→OTCP, so the double turntable five The overall complete kinematic model of the CNC machine tool with the total coordinate transformation matrix

To represent:

in

represents the rotation matrix of the structural part, p=[p _x p _y p _z ] ^T represents the displacement matrix of the structural part; Described step S2 specifically comprises: S21: Establish a three-dimensional solid model of the double-turntable five-axis CNC machine tool, and use the three-dimensional model to obtain its own mass mi, center of mass coordinates C _i , and inertia tensor _{I i at} its own center of mass C _i ; S22: The translational velocities v _i and rotation velocities w _i of all centroids in the same coordinate system are calculated by the time differential of the homogeneous transformation matrix, and the expressions are as follows:

The kinetic energy of the i-th structural member relative to the inertial coordinate system is E _li , and the inertia tensor matrix I _i of the structural member i, according to the kinetic energy of the differential mass on the structural member, the kinetic energy E of the structural member of the double-turntable five-axis CNC machine tool is obtained _l is:

Denote the driving rotor of the motor on the i-th structural member as I _zi , then the sum of the rotational kinetic energy of the n rotors of the double turntable five-axis CNC machine tool is:

To sum up, it can be concluded that the overall kinetic energy of the dual-turntable five-axis CNC machine tool is the sum of the kinetic energy of the drive shaft rotor and the kinetic energy of the structural parts:

S23: The total potential energy of the double-turntable five-axis CNC machine tool is:

where g is the gravity vector in the inertial coordinate system, and G _i is the center of mass coordinate of the structural member i; S24: Construct the Lagrange function L of a five-axis CNC machine tool with a double turntable: L=E _k -E _p (8) By derivation of the above formula, the Lagrange equation of the dynamics of the dual-turntable five-axis CNC machine tool can be obtained:

Substitute the kinetic energy and potential energy into the Lagrange function constructed by (9), and arrange it as follows:

The above formula is simplified to:

where M(q) is the mass matrix of each structural member,

are centrifugal force and Coriolis force vector, G(q) is the gravity vector matrix of the structural part, F is the applied force vector formed by the friction force and cutting force generated in the cutting process, M(q),

They are represented by the relevant Jacobian matrix as:

Described step S3 specifically comprises: S31: Analyze the force of the spindle system in the milling state, and obtain the average normal force P _n1 of the spindle-tool shank joint as:

Among them, F ₀ is the clamping force of the spindle-tool holder, F _n1 is the normal force of the spindle-tool holder joint, S ₁ is the contact area of the spindle-tool holder, φ ₁ is the included angle of the tool holder, and L ₁ is the spindle- The axial length of the joint part of the tool holder, r ₁ and r ₂ are the large radius and small radius of the joint part, and μ ₁ is the friction coefficient; The equivalent spring stiffness of the joint is obtained by Yoshimura's integral method:

Among them, k(δ) can be obtained by transforming the integral curve of Yoshimura Yutaka, α ₀ and β ₀ are the contact characteristic parameters of the joint, and δ _rm is the radial milling load

The maximum amount of deformation of the internal parts of the joint under the action,

E is the elastic modulus, υ is the Poisson’s ratio, R is the radius of the joint, δ _j is the radial gap of the joint caused by centrifugal force, and when the spindle speed is n, the centrifugal force is

b is the outer diameter of the main shaft; S32: Perform force analysis on the spindle-bearing joint in the milling state. According to Hertz theory, the force balance equation of the t-th rolling element of the bearing is:

where Q _it and Q _ot are the contact loads between the rolling element and the inner and outer rings, α _it and α _ot are the contact angles between the rolling element and the inner and outer rings, M _gt is the gyroscopic moment, F _ct is the centrifugal force, and D is the diameter of the rolling element; Perform an overall force analysis on the bearing:

where _Ri is the radius of the inner raceway curvature center circle, ri is the radius of the inner raceway, F _rx is the radial load _on the front and rear spindle-bearing joints, and the radial load on the front spindle-bearing joint

Radial load on the rear spindle-bearing joint

γ _t The t-th rolling element is the azimuth angle, and z is the number of rolling elements in the bearing; The Newton-Raphson iteration method is used to solve the equation system, and the contact stiffness matrix of the spindle-bearing joint is obtained; S33: Establish the mechanical balance equation of the joint of the rolling linear guide in the milling state:

Among them, M _x , My _y and M _z are the three-way torques of x, y and z, respectively, P _x and P _y are the overall component forces acting on the x and y directions of the guide rail pair, and F _qz is the ball screw pair. Traction force, G ₁ is the weight of the tool holder, G ₂ is the overall weight of the guide rail pair; The joint part between the guide rail and the slider is divided into four areas, and the decomposition load generated when each reaction force and reaction moment acts independently is evenly distributed to the joint part between the slider and the guide rail, which can be obtained after the cumulative processing of the following formula Normal force and tangential force acting on each joint:

Wherein i, j=1, 2 represent the number of each joint respectively, P _xij (n), P _yij (n) are each reaction force or moment acting alone to generate component force at the joint; Only consider the normal force acting on the guide rail to calculate the internal force of the rolling linear guide: (F ₁ -F ₃ )n sinγ=F _y /2 (20)

Among them, n is the number of balls in a single row of tracks, F _P is the normal component force of the preload acting on the balls, and γ is the angle formed by the contact between the balls and the raceway; According to the Hertz contact theory, the contact changes between the ball and the slider, and between the ball and the guide rail are:

where E ₁ , E ₂ , E ₃ and μ ₁ , μ ₂ , μ ₃ represent the elastic modulus and Poisson’s ratio of the ball, slider and rolling linear guide materials, respectively, ∑ρ is the sum of the principal curvatures at the internal contact points, ∑ ρ=ρ ₁ +ρ ₂ +ρ ₃ +ρ ₄ , and ρ ₁ =ρ ₂ =2/d _b , ρ ₃ =−f/d _b ,ρ ₄ =0, _db is the ball diameter, and f is the raceway The ratio of the radius of curvature to the diameter of the ball, the value of J/m _a can be obtained by looking up the table by calculating the value of τ, and τ=|ρ ₃ -ρ ₄ |/∑ρ; Then the normal and tangential contact stiffnesses of the rail joint are:

where α is the angle between the normal force of the rolling element and the longitudinal axis; S34: Take the Z-axis ball screw joint as an example, establish a mechanical model of the joint in the milling state, and further analyze to obtain the displacement balance equation:

By analyzing the force of the rolling elements of the ball screw motion pair, the force balance equation of the rolling elements is obtained:

where Q _t is the contact load of the rolling element, f _tx , f _ty , and f _tz are the force on the kth rolling element,

is the azimuth angle of the t-th rolling element, and ψ is the helix angle of the screw raceway; Under the action of the milling load, the force analysis between the rolling elements and the screw raceway in the ball screw kinematic pair is carried out, and the mechanical balance equation between all the rolling elements and the screw raceway is established as:

Through the force balance formula of each rolling element, the contact force of all rolling elements is accumulated, the resultant force is derived from the displacement, and the contact stiffness matrix of the joint part of the ball screw kinematic pair in the milling state is obtained; Described step S4 specifically comprises: A complete multi-body dynamic model of the dual-turntable five-axis CNC machine tool is established by combining the dynamic equations of the dual-turntable five-axis CNC machine tool and the contact characteristic parameters of the main joints, which is represented by the following differential equation:

Among them, K(q) is the contact stiffness matrix of the joint, and the equations are solved by combining the parameters of the components of the dual-turntable five-axis machine tool (11), (15), (17), (23), (26).

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