Method for simulating rotation error of aerostatic spindle under influence of speed effect

Abstract

The invention discloses an aerostatic spindle rotation error simulation method under the influence of a speed effect, which considers the influence of centrifugal force, gyroscopic effect and other speed effects on spindle rotation errors, and establishes an aerostatic bearing-rotor system dynamic model under the influence of the speed effect to obtain a spindle rotation trajectory to research the spindle rotation errors. The method comprises the following steps: establishing an air static pressure bearing-rotor system model according to the structure and working principle of an air static pressure main shaft; establishing a dynamic matrix model of the aerostatic bearing-rotor system under the influence of the speed effect according to the vibration characteristics of the main shaft; processing the vibration signal to obtain an amplitude-frequency curve of the main shaft system under the influence of the speed effect; the translation displacement and deflection angle of the spindle vibration are superposed, a rotation track of a bearing-rotor system under the influence of the speed effect is established, and then the influence of the speed effect on the rotation error of the aerostatic spindle is researched according to the result.

Description

Technical Field

[0001] The invention relates to a simulation method, which is suitable for studying the influence of speed effect on the rotation error of an air static pressure spindle and realizing the precision analysis in the working process of a spindle system. Background Art

[0002] The aerostatic spindle is a key operating component of a machining machine. Its rotation error plays a crucial and decisive role in the machining accuracy of the machine tool, and is also a key parameter for evaluating the dynamic performance of the machine tool. The spindle rotation error will lead to a decrease in the machining quality of the machine tool. Therefore, it is particularly important to conduct an in-depth analysis of the spindle rotation error. In the actual working process of the spindle, due to the increase in speed, centrifugal force, gyroscopic effect and other speed effects will be caused, which will affect the aerostatic spindle rotation error. In this process, the aerostatic spindle will translate and tilt, thereby generating a rotation error. The aerostatic spindle rotation error includes radial runout error, axial runout error and angular error. The axial runout error and angular error have a greater impact on the machining surface quality. How to introduce the speed effect into the vibration analysis of the aerostatic spindle and combine the two errors to establish the rotation trajectory of the bearing-rotor system is a difficult problem in the study of the aerostatic spindle rotation error.

[0003] The rotation trajectory of the air static pressure bearing-rotor system under the influence of speed effect is established, which reflects the influence of speed effect on spindle accuracy in a more intuitive way. During the operation of the spindle, its movement will be disturbed by various internal and external factors such as external load, manufacturing error and speed effect, causing unbalanced movement of the entire spindle system. Analyzing the spindle vibration signal can evaluate and analyze the stable state of the spindle system under the influence of speed effect. Summary of the invention

[0004] In view of the problem that the rotation error of an aerostatic spindle under the influence of speed effect affects the machining accuracy, the present invention provides a simulation method for the rotation error of an aerostatic spindle under the influence of speed effect. The present invention establishes a set of aerostatic spindle vibration simulation research methods by considering speed effects such as centrifugal force and gyroscopic effect, describes the rotation trajectory of the aerostatic bearing-rotor system, and simultaneously connects various dynamic parameters of the spindle during operation with the vibration signal to achieve synchronous analysis of the aerostatic spindle vibration error and system stability.

[0005] A method for simulating air static pressure spindle rotation error under the influence of speed effect, the method comprising the following steps:

[0006] (1) Establish an aerostatic bearing-rotor system model.

[0007] During the operation of the aerostatic spindle, the air film between the bearing and the rotor plays a supporting and lubricating role. Compared with the spindle rotor, the stiffness of the bearing air film is lower. Therefore, the air film is simplified to a uniformly distributed spring damping system, and each exhaust cavity is simplified to a spring damping system with two degrees of freedom in the X and Y directions. The bearing-rotor system model is established, as shown in Figure 1 As shown, through the force analysis of the bearing-rotor system, the dynamic equation under the influence of centrifugal force, gyroscopic effect and other speed effects is obtained, as shown in the following formula:

[0008]

[0009] Where m is the mass of the shaft, and are the vibration speeds in the X and Y directions respectively, and are the resultant external forces in the X and Y directions, F x and F y are the radial external loads along the X and Y directions respectively, e is the eccentricity of the eccentric mass, Fr is the radial external load, ω is the rotor angular velocity, where meω 2 cos(ωt), meω 2 sin(ωt) represents the centrifugal force, Represents the effect of gyroscopic effect.

[0010] (2) Establish the dynamic matrix model of the aerostatic bearing-rotor system as follows:

[0011]

[0012] Where x and y are the vibration displacements in the X and Y directions, respectively. and are the vibration accelerations in the X and Y directions, respectively. T is the sum of the damping coefficients in the X direction, T′ is the sum of the stiffness coefficients in the X direction, P is the sum of the damping coefficients in the Y direction, and P′ is the sum of the stiffness coefficients in the Y direction. It can be obtained by formula (3), where Ki is the stiffness coefficient and Ci is the damping coefficient. Equation (2) is numerically solved on the MATLAB software platform to obtain a comparison chart of the vibration displacements in the X and Y directions under the influence of velocity effects such as centrifugal force and gyroscopic effect and the vibration displacement without considering the velocity effect, as shown in Figure 2a ), Figure 2b ), Figure 2a ) is the comparison diagram of vibration displacement in X direction, Figure 2b ) is a comparison diagram of vibration displacement in the Y direction.

[0013]

[0014] (3) Use Fourier transform to process the time domain signal to obtain the time domain characteristics and frequency domain characteristic parameters of the signal. The principle is as follows:

[0015]

[0016] In the formula, F(t) is the image function of f(t), and f(t) is the original image function of F(ω), which is also the vibration signal of the spindle rotor. By processing the vibration signal, the amplitude-frequency curve under the influence of speed effects such as centrifugal force and gyro effect of the spindle system is compared with the amplitude-frequency curve without considering the speed effect, as shown in Figure 3 shown.

[0017] (4) The vibration error in the X and Y directions is composed of the superposition of translational displacement and deflection angle, which further constitutes the rotational error, as shown in the following formula:

[0018]

[0019] Where x and y are the vibration displacements in the X and Y directions, respectively. are the deflection angles of the spindle in the X and Y directions, Δx and Δy are the displacements of the outermost end of the spindle axis in the X and Y directions, i.e., the vibration errors, and ΔE is the spindle rotation error. Based on the established bearing-rotor dynamics model and the corresponding dynamics matrix model, the corresponding function files are written through MATLAB software to solve the ordinary differential equations to obtain the vibration displacements in the X and Y directions, and then the rotation trajectory of the corresponding aerostatic bearing-rotor system under the influence of speed effects such as centrifugal force and gyroscopic effect can be compared with the rotation trajectory without considering the speed effect, as shown in the figure below: Figure 4 shown.

[0020] Compared with the prior art, the present invention has the following advantages:

[0021] The present invention describes the rotation trajectory of the aerostatic bearing-rotor system under the influence of speed effect, introduces speed effects such as centrifugal force and gyroscopic effect into the aerostatic spindle vibration analysis, and more intuitively reflects the influence of speed effect on spindle rotation error by comparing the rotation trajectory with and without considering speed effect. And by changing the spindle speed to obtain different rotation trajectories, the influence of speed on rotation error is studied.

[0022] By establishing a bearing-rotor dynamics model, the vibration error of the spindle is obtained, and the vibration signal is processed to obtain the amplitude-frequency curve of the spindle system under the influence of the speed effect, and the numerical range of the natural frequency of the spindle system is determined to avoid resonance. This method has high computational efficiency and strong versatility, and provides a model and basis for the study of spindle rotation error in actual machine tool processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1It is the aerostatic bearing-rotor system model.

[0024] Figure 2 is a comparison of displacements under the influence of velocity effects in the X and Y directions. Figure 2a ) Vibration displacement in the X direction, Figure 2b ) is the vibration displacement in the Y direction.

[0025] Figure 3 This is a comparison diagram of the resonance state under the speed effect.

[0026] Figure 4 This is a comparison diagram of the rotation trajectory under the speed effect. DETAILED DESCRIPTION

[0027] The method of the present invention is implemented by a software program installed on a computer. MATLAB software is installed on the computer.

[0028] The method of the present invention specifically comprises the following steps:

[0029] Step 1, establishing an aerostatic bearing-rotor system model;

[0030] Step 2, establishing a dynamic matrix model of the aerostatic bearing-rotor system;

[0031] It can be seen from Figure 2 that as the spindle speed increases, the vibration displacement amplitude of the spindle in the X and Y directions gradually increases. Comparing the vibration amplitudes of the spindle at different speeds, it is found that the amplitude obtained by coupling centrifugal force and gyroscopic effect is significantly greater than the amplitude obtained without considering the speed effect, and the speed effect condition is more in line with the actual working conditions. Therefore, in the design optimization process of the spindle, the influence of the speed effect on the vibration characteristics of the spindle system must be considered.

[0032] Step 3, processing the vibration signal to obtain the amplitude-frequency curve of the spindle system;

[0033] from Figure 3 It can be seen that the resonance amplitude of the spindle without considering the speed effect is smaller than the resonance amplitude considering the speed effect, which means that when resonance occurs, the speed effect will aggravate the impact of the resonance on the spindle and cause more serious damage.

[0034] Step 4: Superimpose the translational displacement and deflection angle of the main shaft vibration to establish the rotation trajectory of the aerostatic bearing-rotor system.

[0035] from Figure 4 It can be seen that with the increase of the speed, the rotation trajectory of the spindle becomes more complicated when the speed effect is considered, and compared with the rotation trajectory without considering the speed effect, the center of the approximate circle of the spindle rotation trajectory is offset. The speed effect increases the rotation error of the spindle, and with the increase of the spindle speed, the rotation error becomes larger and larger.

Claims

1. A method for simulating the rotation error of an air static pressure spindle under the influence of speed effect, characterized in that: The steps include: Step 1, establishing an aerostatic bearing-rotor system model; Step 2, establishing a dynamic matrix model of the aerostatic bearing-rotor system; Step 3, processing the vibration signal to obtain the amplitude-frequency curve of the spindle system; Step 4: Superimpose the translational displacement and deflection angle of the main shaft vibration to establish the rotation trajectory of the aerostatic bearing-rotor system.

2. The method for simulating the air static pressure spindle rotation error under the influence of speed effect according to claim 1, characterized in that: The method comprises the following steps, (1) Establish an aerostatic bearing-rotor system model; During the operation of the aerostatic spindle, the air film between the bearing and the rotor plays a supporting and lubricating role. The air film is simplified into a uniformly distributed spring damping system, and each exhaust cavity is simplified into a spring damping system with two degrees of freedom in the X and Y directions. The bearing-rotor system model is established. Through the force analysis of the bearing-rotor system, the dynamic equation under the influence of centrifugal force, gyroscopic effect and other speed effects is obtained, as shown in the following formula: Where m is the mass of the shaft, and are the vibration speeds in the X and Y directions, respectively, X合 and F Y合 are the resultant external forces in the X and Y directions, F x and F y are the radial external loads along the X and Y directions respectively, e is the eccentricity of the eccentric mass, Fr is the radial external load, ω is the rotor angular velocity, where meω 2 cos(ωt), meω 2 sin(ωt) represents the centrifugal force, Represents the role of gyroscopic effect; (2) Establish the dynamic matrix model of the aerostatic bearing-rotor system as follows: Where x and y are the vibration displacements in the X and Y directions, respectively. and are the vibration accelerations in the X and Y directions respectively; T is the sum of the damping coefficients in the X direction, T′ is the sum of the stiffness coefficients in the X direction, P is the sum of the damping coefficients in the Y direction, and P′ is the sum of the stiffness coefficients in the Y direction; obtained by formula (3), where Ki is the stiffness coefficient and Ci is the damping coefficient; equation (2) is numerically solved on the MATLAB software platform to obtain a comparison diagram of the vibration displacements in the X and Y directions under the influence of velocity effects such as centrifugal force and gyroscopic effect and the vibration displacement without considering the velocity effect; (3) Use Fourier transform to process the time domain signal and obtain the time domain characteristics and frequency domain characteristic parameters of the signal, as shown in the following formula: Where, F(t) is the image function of f(t), f(t) is the original image function of F(ω), and is also the vibration signal of the spindle rotor. The vibration signal is processed to obtain the amplitude-frequency curve under the influence of speed effects such as centrifugal force and gyro effect of the spindle system and the comparison diagram of the amplitude-frequency curve without considering the speed effect. (4) The vibration error in the X and Y directions is composed of the superposition of translational displacement and deflection angle, which further constitutes the rotational error, as shown in the following formula: Where x and y are the vibration displacements in the X and Y directions, respectively. are the deflection angles of the spindle in the X and Y directions, Δx and Δy are the displacements of the outermost end of the spindle axis in the X and Y directions, namely the vibration errors, and ΔE is the spindle rotation error. Based on the established bearing-rotor dynamics model and the corresponding dynamics matrix model, the corresponding function files are written through MATLAB software to solve the ordinary differential equations to obtain the vibration displacements in the X and Y directions, and then the rotation trajectory of the corresponding aerostatic bearing-rotor system under the influence of speed effects such as centrifugal force and gyroscopic effect is compared with the rotation trajectory without considering the speed effect.

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