CN110308701A - A Motion Accuracy Prediction Method for Direct-Drive High-speed Feed System Considering Thrust Harmonic Characteristics - Google Patents

Abstract

A method for predicting motion accuracy of a direct-drive high-speed feed system considering thrust harmonic characteristics provided by the present invention includes the following steps: Step 1: According to the motion accuracy analysis model of direct-drive high-speed feed system considering thrust harmonic characteristics, the system is obtained Disturbance transfer function; step 2, extract the characteristic equation according to the system disturbance transfer function obtained in step 1; step 3, bring the actual system parameters into the characteristic equation obtained in step 2, and obtain the root of the characteristic equation, and the root of the characteristic equation Discrimination; step four, according to the discrimination result in step three, using the system disturbance transfer function G _r (s) obtained in step one, through inverse Laplace transform, to obtain the system motion accuracy under the action of single thrust harmonic; step Five, repeat step 4 to obtain the motion accuracy of the direct-drive high-speed feed system of all thrust harmonics; the present invention directly extends the linear motor thrust fluctuation problem in the traditional analysis to the motion accuracy of the final feed system, for further evaluation of the linear motor The degree of influence of the thrust fluctuation phenomenon in the actual CNC machine tool has important guiding significance.

Description

Motion accuracy prediction of a direct-drive high-speed feed system considering thrust harmonic characteristics method

technical field

The invention belongs to the field of motor drive and control, and in particular relates to a method for predicting motion accuracy of a direct-drive high-speed feed system in consideration of thrust harmonic characteristics, which is suitable for occasions such as high-speed high-precision numerical control machine tools.

Background technique

The permanent magnet synchronous linear motor feed system realizes zero feed transmission. Compared with the traditional ball screw feed system, it has the advantages of large thrust, high speed and good precision. It has a wide range of applications in many fields such as high-speed high-precision CNC machine tools. Application prospects. However, the zero-gear structure also has many disadvantages, the most prominent of which is the thrust fluctuation caused by the non-linearity of the drive circuit and the motor structure. Aiming at thrust fluctuation, scholars at home and abroad have carried out a lot of research work, and put forward a variety of methods around motor structure optimization and control compensation algorithm, which are of great value and significance for improving thrust fluctuation.

The direct-drive high-speed feed system cancels all intermediate mechanical transmission links, and the thrust harmonics directly act on the mechanical system. Although the structure has been optimized and control compensation has been performed, it is difficult to completely eliminate thrust fluctuations caused by various factors. Compared with the traditional ball screw feed system, the thrust harmonic still has a more significant impact on the system motion accuracy. The traditional thrust harmonic analysis and calculation method is only aimed at the permanent magnet synchronous linear motor itself, and does not extend its influence to the final motion accuracy of the feed system. Although with the help of some numerical simulation software, the system output response under the action of thrust harmonics can be obtained, but this method takes time to calculate, and the analysis results cannot explain the internal mechanism of thrust harmonic action, and it is not convenient to discuss different servo control parameters and loads. It is difficult to quickly and effectively analyze the sensitive parameters affected by thrust harmonics due to the influence of thrust harmonics of different frequencies on the motion accuracy of the system. If a fast and accurate analytical calculation method for the motion accuracy of the direct-drive high-speed feed system considering the thrust harmonic characteristics can be established, it will be of great value and significance for further optimizing the servo parameters and constructing the control compensation strategy.

Contents of the invention

The purpose of the present invention is to provide a method for predicting motion accuracy of a direct-drive high-speed feed system considering the characteristics of thrust harmonics, which solves the problems of time-consuming and difficult analysis and calculation methods for thrust harmonics of direct-drive high-speed feed systems in the prior art. Quickly and effectively analyze the problem of sensitive parameters affected by thrust harmonics.

In order to achieve the above object, the technical scheme adopted in the present invention is:

A method for predicting motion accuracy of a direct-drive high-speed feed system considering thrust harmonic characteristics provided by the present invention includes the following steps:

Step 1, according to the motion accuracy analysis model of the direct-drive high-speed feed system considering the thrust harmonic characteristics, the system disturbance transfer function is obtained;

Step 2, extracting the characteristic equation according to the system disturbance transfer function obtained in step 1;

Step 3, bringing actual system parameters into the characteristic equation obtained in step 2, obtaining the root of the characteristic equation, and discriminating the root of the characteristic equation;

Step 4, according to the discrimination result in step 3, using the system disturbance transfer function G _r (s) obtained in step 1, through inverse Laplace transform, to obtain the motion accuracy of the system under the action of a single thrust harmonic;

Step 5, repeat step 4 to obtain the motion accuracy of the direct-drive high-speed feed system for all thrust harmonics.

Preferably, in step 1, the expression of the system disturbance transfer function G _r (s) is:

Among them, G _r (s) is the system disturbance transfer function, s is the Laplacian operator, x _o (s) is the system output response, F _tr (s) is the motor thrust harmonic, K _p is the position loop proportional gain , K _v is the proportional gain of the speed loop, T _v is the integral time of the speed loop, K _A is the equivalent proportional gain of the current loop, K _F is the thrust constant of the motor, and m is the mass of the driving load.

Preferably, in step 2, the expression of the characteristic equation is:

as ³ +bs ² +cs+d＝0

Wherein, a=m, b=K _v K _F , c=K _v K _F /T _v +K _F K _v K _p , d=K _p K _v K _F /T _v .

Preferably, in step three, the specific method for discriminating the root of the characteristic equation is:

When D=b ² -3ac<0, the characteristic equation has one real root and two conjugate imaginary roots;

When D=b ² -3ac>0, and When , the characteristic equation has one real root and two conjugate imaginary roots;

When D=b ² -3ac>0, and , the characteristic equation has three real roots.

Preferably, in step 4, the expression of the motion accuracy of the system under the action of a single thrust harmonic is:

x _tr0 (t)＝L ^-1 [G _r (s) · F _tr (s)]

Among them, L ^-1 represents the inverse Laplace transform, and F _tr (s) is the complex domain form of the thrust harmonic.

Preferably, in step five, the expression of the motion accuracy of the direct-drive high-speed feed system for all thrust harmonics is:

Compared with prior art, the beneficial effect of the present invention is:

The present invention provides a method for predicting motion accuracy of direct-drive high-speed feed systems that considers thrust harmonic characteristics. By directly extending the linear motor thrust fluctuation problem in traditional analysis to the motion accuracy of the final feed system, it is useful for further evaluation of linear motors. The degree of influence of the thrust fluctuation phenomenon in the actual CNC machine tool has important guiding significance. Moreover, the calculation method can accurately obtain the analytical solution of the motion output response of the direct-drive high-speed feed system under the action of multi-frequency thrust harmonic disturbance, and use the calculation results to conveniently discuss the impact of different servo control parameters and different frequency thrust harmonics under load. The influence law of system motion accuracy can effectively analyze the sensitive parameters affected by thrust harmonics, especially for further optimizing servo parameters and constructing control compensation strategies.

Description of drawings

Figure 1 is the analysis model of the motion accuracy of the direct-drive high-speed feed system;

Fig. 2 is the test result of the motion stability of the direct-drive high-speed feed system considering the thrust harmonic effect.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings.

A method for predicting motion accuracy of a direct-drive high-speed feed system considering thrust harmonic characteristics provided by the present invention includes the following steps:

Step 1: Establish the motion accuracy analysis model of the direct-drive high-speed feed system considering the thrust harmonic characteristics, and obtain the system disturbance transfer function G _r (s), namely

Among them, G _r (s) is the system disturbance transfer function, s is the Laplacian operator, x _o (s) is the system output response, F _tr (s) is the motor thrust harmonic, K _p is the position loop proportional gain , K _v is the proportional gain of the speed loop, T _v is the integral time of the speed loop, K _A is the equivalent proportional gain of the current loop, K _F is the thrust constant of the motor, and m is the mass of the driving load.

The motion accuracy analysis model of direct-drive high-speed feed system considering thrust harmonics includes position loop, speed loop, current loop, linear motor, drive components and feedback components. The position loop adopts proportional control, the speed loop adopts proportional integral control, and the current The loop is equivalent to a proportional gain, the thrust harmonic generated by the linear motor is introduced into the model in the form of interference, the mechanical system is equivalent to a single inertia system, and the closed-loop feedback loop gain is 1.

Step 2: According to the transfer function obtained in Step 1, extract the characteristic equation, namely

as ³ +bs ² +cs+d＝0

Where: a=m,b=K _v K _F ,c=K _v K _F /T _v +K _F K _v K _p ,d=K _p K _v K _F /T _v

Bring the actual system parameters into the characteristic equation obtained in step 2, obtain the root of the characteristic equation, and discriminate the root of the characteristic equation;

Among them, the actual system parameters include position loop proportional gain, speed loop proportional gain and integral time, motor thrust constant and system driving load.

The specific method for discriminating the root of the characteristic equation is:

When D=b ² -3ac<0, the characteristic equation has one real root and two conjugate imaginary roots;

When D=b ² -3ac>0, and When , the characteristic equation has one real root and two conjugate imaginary roots;

When D=b ² -3ac>0, and , the characteristic equation has three real roots.

Step 3: According to the condition of the root of the characteristic equation obtained in step 2, using the disturbance transfer function obtained in step 1, through inverse Laplace transform, the motion accuracy of the system under the action of a single thrust harmonic is obtained, namely

x _tr0 (t)＝L ^-1 [G _r (s) · F _tr (s)]

Step 4: Repeat Step 3 to obtain the motion accuracy of the direct-drive high-speed feed system for all thrust harmonics, namely

Example

In this embodiment, a single-axis feed test bench equipped with a direct drive feed system is selected. The maximum feed speed of the test bench is 30m/min, and the maximum acceleration is 1g. Specific steps are as follows:

Step 1: Establish a direct-drive high-speed feed system motion accuracy analysis model considering thrust harmonic characteristics, as shown in Figure 1, specifically including position loop, speed loop, current loop, linear motor, drive components and feedback components, among which, The position loop adopts proportional control; the speed loop adopts proportional integral control; the current loop is equivalent to proportional gain; the thrust harmonic generated by the linear motor is introduced into the model in the form of interference; the mechanical system is equivalent to a single inertia system, and the closed-loop feedback loop gain is 1 .

According to the established motion precision analysis model, the system disturbance transfer function is obtained, namely

Among them, G _r (s) is the system disturbance transfer function, s is the Laplacian operator, x _o (s) is the system output response, F _tr (s) is the motor thrust harmonic, K _p is the position loop proportional gain , K _v is the proportional gain of the speed loop, T _v is the integral time of the speed loop, K _A is the equivalent proportional gain of the current loop, K _F is the thrust constant of the motor, and m is the mass of the driving load.

Step 2: According to the transfer function obtained in Step 1, extract the characteristic equation, namely

as ³ +bs ² +cs+d＝0

Among them, a=m, b=K _v K _F , c=K _v K _F /T _v +K _F K _v K _p , d=K _p K _v K _F /T _v

Bring the actual system parameters into the characteristic equation obtained in step 2, obtain the root of the characteristic equation, and discriminate the root of the characteristic equation;

Among them, the actual system parameters include position loop proportional gain, speed loop proportional gain and integral time, motor thrust constant and system driving load.

The specific method for discriminating the root of the characteristic equation is:

When D=b ² -3ac<0, the characteristic equation has one real root and two conjugate imaginary roots;

When D=b ² -3ac>0, and When , the characteristic equation has one real root and two conjugate imaginary roots;

When D=b ² -3ac>0, and , the characteristic equation has three real roots.

Step 3: Assume that the thrust harmonics in the linear motor are multiple periodic sinusoidal forms, and the final output response is the superposition of multiple harmonics. In order to simplify the calculation process, choose one of them, namely

The corresponding Laplace transform is:

Using the disturbance transfer function obtained in step 1, the motion accuracy in the complex domain under the action of a single thrust harmonic is obtained, namely

According to the condition of the root of the characteristic equation obtained in step 2, the motion accuracy of the system under the action of a single thrust harmonic is obtained by inverse Laplace transform, namely

When the characteristic equation has one real root and two conjugate imaginary roots, the motion accuracy of the system under the action of a single thrust harmonic is:

When the characteristic equation has three real roots, the motion accuracy of the system under the action of a single thrust harmonic is:

In the formula, each item is a coefficient which can be obtained by inverse Laplace transform, and s ₁ , s ₂ , s ₃ are the three roots of the characteristic equation respectively.

Step 4: Repeat Step 3 to obtain the motion accuracy of the direct-drive high-speed feed system considering all thrust harmonics, that is, when the characteristic equation has one real root and two conjugate imaginary roots, the motion accuracy of the system considering all thrust harmonics is :

When the characteristic equation has three real roots, the motion accuracy of the system considering all thrust harmonics is:

The actual motion accuracy of the high-speed direct-drive motion system is tested by using a laser interferometer with a frequency of 1KHz and a feed speed of 20m/min.

Extract the steady-state displacement fluctuation error item in the motion accuracy, perform Fourier transform on it, and compare the experimental test results and theoretical calculation results at different frequencies, as shown in Figure 2; it can be seen from Figure 2 that the system's steady-state displacement The maximum deviation of the theoretical and experimental results of fluctuation is only 4%, which proves the accuracy and reliability of the calculation method proposed by the present invention.

Claims (6)

1. a kind of direct-drive high-speed feed system kinematic accuracy prediction technique for considering thrust harmonic characterisitic, which is characterized in that including Following steps:

It is dry to obtain system according to the direct-drive high-speed feed system kinematic accuracy analysis model for considering thrust harmonic characterisitic for step 1 Disturb transmission function；

Step 2, the system interference transmission function obtained according to step 1 extract characteristic equation；

Step 3 brings real system parameter in characteristic equation obtained in step 2 into, the root of characteristic equation is obtained, to feature Equation root is differentiated；

Step 4, according to differentiating as a result, the system interference transmission function obtained using step 1, passes through La Pula in step 3 This inverse transformation obtains the system motion precision under single thrust harmonic wave effect；

Step 5 repeats step 4, obtains the direct-drive high-speed feed system kinematic accuracy of all thrust harmonic waves.

2. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1 Method, which is characterized in that in step 1, system interference transmission function G_r(s) expression formula are as follows:

Wherein, G_rIt (s) is system interference transmission function, s is Laplace operator, x_oIt (s) is system output response, F_trIt (s) is electricity Machine thrust harmonic wave, K_pFor position ring proportional gain, K_vFor velocity loop proportional gain, T_vFor the speed ring time of integration, K_AFor electric current loop Equieffective ratio gain, K_FFor motor thrust constant, m is driving load quality.

3. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1 Method, which is characterized in that in step 2, the expression formula of characteristic equation are as follows:

as³+bs²+ cs+d=0

Wherein, a=m, b=K_vK_F, c=K_vK_F/T_v+K_FK_vK_p, d=K_pK_vK_F/T_v。

4. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1 Method, which is characterized in that in step 3, the specific method differentiated to the root of characteristic equation is:

Work as D=b²When -3ac < 0, characteristic equation has a real root and two conjugation imaginary roots；

Work as D=b²- 3ac > 0, andWhen, characteristic equation has a real root and two conjugation imaginary roots；

Work as D=b²- 3ac > 0, andWhen, there are three real roots for characteristic equation.

5. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1 Method, which is characterized in that in step 4, the expression formula of the system motion precision under single thrust harmonic wave effect are as follows:

x_tr0(t)=L^-1[G_r(s)·F_tr(s)]

Wherein, L^-1Indicate inverse Laplace transformation, F_trIt (s) is the complex field form of thrust harmonic wave.

6. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1 Method, which is characterized in that the direct-drive high-speed feed system kinematic accuracy in step 5, under all thrust harmonic wave effects are as follows: