CN110231775A - A kind of accurate prediction technique of direct-drive high-speed feed system kinematic accuracy considering mechanical twisting oscillation - Google Patents

Abstract

A method for accurately predicting the motion accuracy of a direct-drive high-speed feed system considering mechanical torsional oscillations provided by the present invention comprises the following steps: Step 1, according to the analysis model of the motion accuracy of the direct-drive high-speed feed system considering mechanical torsional oscillations, the mechanical system is obtained The disturbance transfer function of torsional oscillation in three directions; Step 2, extract the characteristic equation according to the 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, The root of the characteristic equation is discriminated; step 4, using the system disturbance transfer function obtained in step 1 and the discrimination result in step 3, obtains the system motion accuracy considering mechanical torsional oscillation; the present invention can discuss different servo control parameters and Under the action of thrust harmonics at different frequencies, the influence of various structural parameters of the mechanical system on the motion accuracy of the system is of great value and significance for the realization of the electromechanical integration design of the direct drive feed system and the active optimization of the mechanical structure.

Description

Precise prediction of kinematic accuracy of a direct-drive high-speed feed system considering mechanical torsional oscillation test method

technical field

The invention belongs to the field of motor drive and control, and in particular relates to a method for accurately predicting motion precision of a direct-drive high-speed feed system considering mechanical torsional oscillations.

Background technique

The permanent magnet synchronous linear motor feed system cancels all intermediate mechanical transmission links, and can realize "zero transmission" of feed motion. It has the advantages of simple structure, high rigidity, high feed speed and acceleration, and good motion performance. It is used in robots, It has good application prospects in rail transit, high-speed machine tools and other fields. However, the direct drive structure also has many significant disadvantages, such as large thrust fluctuations, sensitivity to interference, high cost, and difficult control. Scholars at home and abroad have conducted a lot of research work on various problems in the direct drive feed system, and proposed a variety of control compensation methods. These methods are of great significance for improving the thrust fluctuation and motion accuracy of the direct drive feed system. . However, in the current research work, the mechanical link of the direct-drive feeding system is simplified to a simple single-inertia system, ignoring the dynamic characteristics of the mechanical system. Numerous field experiments show that the mechanical transmission link of the direct-drive feed system is not an ideal single-inertia link, and there are various forms of vibration modes due to the influence of the dynamic characteristics of the joint of the guide rail slider. Neglecting the impact of these mechanical torsional vibrations on the motion accuracy of the system, the theoretical calculation results obtained by the established correlation analysis model have a large deviation from the actual, which is difficult to meet the engineering requirements. In addition, due to the lack of relevant theoretical basis, it is difficult to realize the active design of the mechanical structure design and selection of the current direct-drive feeding system, which restricts the practical application and popularization of the direct-drive system.

Contents of the invention

The purpose of the present invention is to propose a method for accurately predicting the motion accuracy of a direct-drive high-speed feed system that considers mechanical torsional oscillations. For the direct-drive high-speed feed system, it solves the theory of motion accuracy caused by ignoring the mechanical dynamic characteristics in the prior art There is a large deviation between the analysis results and the actual situation, which can provide a theoretical basis for the active design of mechanical systems oriented to motion requirements.

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

A method for accurately predicting motion accuracy of a direct-drive high-speed feed system considering mechanical torsional oscillations provided by the present invention includes the following steps:

Step 1, according to the direct-drive high-speed feed system motion accuracy analysis model considering mechanical torsional oscillation, the interference transfer function of the torsional oscillation in the three directions of the mechanical system is obtained;

Step 2, extracting the characteristic equation according to the interference 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: Using the system disturbance transfer function obtained in Step 1 and the discrimination result in Step 3, the motion accuracy of the system considering the mechanical torsional oscillation is obtained.

Preferably, in step 1, the expression of the disturbance transfer function of the torsional oscillation in three directions of the mechanical system is:

Among them, G _rp (s), G _ry (s) and G _rr (s) are the interference transfer functions of mechanical pitch oscillation, yaw oscillation, and roll oscillation, respectively;

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

where a _p = T _v J _y ; a _y = T _v J _z ; a _r = T _v J _x ; b _p = T _v C _θy + K _v K _F T _v M _p S _p ; b _y = T _v C _θz +K _v K _F T _v M _y S _y ; b _r ＝T _v C _θx +K _v K _F T _v M _r S _r ; c _p ＝T _v K _θy +K _v K _F M _p S _p + K _p K _v K _F T _v M _p S _p ; d _p = K _p K _v K _F T _v M _p S _p ; c _y = T _v K _θz + K _v K _F M _y S _y + K _p K _v K _F T _v M _y S _y ; d _y = K _p K _v K _F T _v M _y S _y ;

c _r = T _v K _θx + K _v K _F M _r S _r + K _p K _v K _F T _v M _r S _r ; d _r = K _p K _v K _F T _v M _r S _r .

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

when When , the characteristic equation has one real root and two conjugate imaginary roots;

when and When , the characteristic equation has one real root and two conjugate imaginary roots;

when and , the characteristic equation has three real roots; i=p, y, r.

Preferably, in step 4, the expression of the system motion accuracy of mechanical torsional oscillation is considered:

x _m0 (t)＝x _Σtrp0 (t)+x _Σtry0 (t)+x _Σtrr0 (t)

Among them, x _Σtrp0 (t), x _Σtry0 (t) and x _Σtrr0 (t) are the system motion output responses caused by mechanical pitch vibration, yaw vibration and roll vibration, respectively.

Preferably, in step four, using the system disturbance transfer function obtained in step one and the discrimination result in step three, the motion accuracy of the system considering mechanical torsional oscillation is obtained, the specific method is:

Using the system disturbance transfer function obtained in step 1, the motion accuracy of the system under the complex number domain under the disturbance is obtained, and the motion accuracy of the system under the complex number domain under the disturbance is processed by the inverse Laplace transform, and according to the step 3 Based on the discriminant results, the motion accuracy of the system considering the mechanical torsional oscillation is obtained.

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

The present invention provides a method for accurately predicting the motion accuracy of a direct-drive high-speed feed system that considers mechanical torsional oscillations. It comprehensively considers the main torsional vibrations of three types of machinery caused by the dynamic characteristics of the guide rail slider joint, and can quickly and effectively take into account the mechanical The motion output response of the direct-drive high-speed feed system under the action of multi-frequency thrust harmonic disturbance of torsional vibration. The calculation results can be used to discuss the impact of various structural parameters of the mechanical system on the system motion accuracy under the action of different servo control parameters and different frequency thrust harmonics. It is of great value and significance to realize the electromechanical integration design of the direct drive feed system and the active optimization of the mechanical structure.

Description of drawings

Figure 1 is an integrated control model of the direct drive feed system considering mechanical torsional vibration;

Figure 2 is an analysis model of the motion accuracy of the direct drive feed system considering the mechanical pitch vibration.

Detailed ways

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

As shown in Figure 1, a method for accurately predicting motion accuracy of a direct-drive high-speed feed system considering mechanical torsional oscillations provided by the present invention includes the following steps:

Step 1: Establish a direct-drive high-speed feed system motion accuracy analysis model considering mechanical torsional oscillations. The model includes position loop, speed loop, current loop, linear motor, drive components and feedback components. The position loop adopts proportional control, and the speed loop adopts proportional control. The loop adopts proportional integral control, the current loop is equivalent to a proportional gain, the closed-loop feedback loop gain is 1, and various interference harmonics are introduced into the model in the form of an equivalent force rectangle.

Mechanical torsional oscillation refers to the torsional vibration around three axes, ignoring the high-order vibration mode and flexible deformation of the mechanical system, namely torsional oscillation, rolling oscillation and pitching oscillation; the mechanical system is equivalent to three second-order torsional vibration systems and a superposition of a single-inertia system.

According to the analytical model, the disturbance transfer function of the torsional oscillation in three directions of the mechanical system is obtained:

Among them, G _rp (s), G _ry (s) and G _rr (s) are the interference transfer functions of mechanical pitch oscillation, yaw oscillation and roll oscillation respectively, s is the Laplacian operator, J _x , J _y , J _z is the moment of inertia of the mechanical system around the three linear axes, K _p is the proportional gain of the position loop, K _v is the proportional gain of the speed loop, T _v is the integral time of the speed loop, K _F is the thrust constant of the motor, M _p , M _y , M _r are equivalent coefficients of disturbance respectively, S _p , Sy _y , S _r are equivalent coefficients of vibration displacement respectively.

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

Where: a _p ＝T _v J _y , a _y ＝T _v J _z , a _r ＝T _v J _x , b _p ＝T _v C _θy +K _v K _F T _v M _p S _p ,

b _y ＝T _v C _θz +K _v K _F T _v M _y S _y ,b _r ＝T _v C _θx +K _v K _F T _v M _r S _r ,

c _p ＝T _v K _θy +K _v K _F M _p S _p +K _p K _v K _F T _v M _p S _p ,d _p ＝K _p K _v K _F T _v M _p S _p ，

c _y = T _v K _θz + K _v K _F M _y S _y + K _p K _v K _F T _v M _y S _y , d _y = K _p K _v K _F T _v M _y S _y ,

c _r ＝T _v K _θx +K _v K _F M _r S _r +K _p K _v K _F T _v M _r S _r ,d _r ＝K _p K _v K _F T _v M _r S _r

There are three situations for the determination of the root of the characteristic equation:

(1) when When , the characteristic equation has one real root and two conjugate imaginary roots;

(2) when and When , the characteristic equation has one real root and two conjugate imaginary roots;

(3) when and , the characteristic equation has three real roots;

where i=p,r,y,

According to the actual system parameters, the condition of the root of the characteristic equation is judged.

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 considering the mechanical torsional oscillation under the disturbance is obtained, namely

x _m0 (t)＝x _Σtrp0 (t)+x _Σtry0 (t)+x _Σtrr0 (t)

In the formula: x _Σtrp0 (t), x _Σtry0 (t) and x _Σtrr0 (t) are the system motion output responses caused by mechanical pitch vibration, yaw vibration and roll vibration, respectively.

Example

A self-designed two-axis cross slide equipped with a direct-drive feed system is selected as an implementation case. Taking the Y-axis as the object, the maximum feed speed is 40m/min, and the maximum acceleration is 1.5g. Specific steps are as follows:

1) Step 1: Establish an integrated control model of direct-drive high-speed feed system considering mechanical torsional oscillation, as shown in Figure 1, specifically including position loop, speed loop, current loop, linear motor, drive components and feedback components, where the position The loop adopts proportional control, the speed loop adopts proportional integral control, the current loop is equivalent to proportional gain, the closed-loop feedback loop gain is 1, and various disturbance harmonics are introduced into the model in the form of equivalent force rectangle; mechanical torsional oscillation refers to: ignoring the mechanical system High-order vibration mode and flexible deformation, torsional vibration around three axes, namely torsional oscillation, roll oscillation and pitch oscillation; the mechanical system is equivalent to the superposition of three second-order torsional vibration systems and a single inertia system.

In order to simplify the calculation process, only the pitch vibration is taken as an example, and the motion accuracy of the direct drive feed system under its influence is considered in the calculation. According to the analysis model, the motion accuracy analysis model is separated from the integrated model, as shown in Figure 2, and the transfer function between the system disturbance and the output response is obtained:

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

a _p s ³ +b _p s ² +c _p s+d _p ＝0

Where: a _p ＝T _v J _y ,b _p ＝T _v C _θy +K _v K _F T _v M _p S _p ,c _p ＝T _v K _θy +K _v K _F M _p S _p +K _p K _v K _F T _v M _p S _p ,d _p ＝K _p K _v K _F T _v M _p S _p

There are three situations for the determination of the root of the characteristic equation:

(1) when When , the characteristic equation has one real root and two conjugate imaginary roots;

(2) when and When , the characteristic equation has one real root and two conjugate imaginary roots;

(3) when and , the characteristic equation has three real roots.

According to the actual system parameters, the condition of the root of the characteristic equation is judged.

Step 3: Use the disturbance transfer function obtained in Step 1 to obtain the motion accuracy of the system in the complex domain under the disturbance:

Step 4: Carry out Laplace inverse transform on the movement accuracy of the system under the complex number domain under the disturbance in step 3, and according to the discrimination of the root of the characteristic equation in step 2, obtain the time of the feed system considering the mechanical torsional oscillation Motion accuracy under the domain:

(1) When the characteristic equation has one real root and two conjugate imaginary roots, the motion accuracy of the feed system in the time domain considering the mechanical torsional oscillation is:

(2) When the characteristic equation has three real roots, the motion accuracy of the feed system in the time domain considering the mechanical torsional oscillation is:

In the formula, the coefficients are jointly determined by the servo control parameters, mechanical parameters and disturbance.

Select two groups of different feed speeds, namely 10m/min and 20m/min, to drive the table to reciprocate back and forth with full stroke. The laser interferometer is used to collect the feed displacement signal and the torsional oscillation signal of the table in real time during the movement of the experimental table. The sampling frequency is 1KHz. Due to the limitation of the test conditions, only the pitch oscillation and yaw oscillation of the table are tested.

The mechanical torsional vibration at different speeds and the feed displacement fluctuations caused by it are shown in Table 1. From attached table 1, it can be seen that during the motion process of the direct drive feed system, due to the interference of various unbalanced torques, there is indeed obvious torsional oscillation, which will cause corresponding feed displacement fluctuations.

Since the experimental object tested in this case has a simple mechanical structure and the reflector of the laser interferometer is installed in the center of the workbench, the maximum displacement fluctuation amplitude caused by torsional oscillation is only about 0.01 μm.

Table 1 The torsional oscillation of the mechanical system and the steady-state displacement fluctuation caused by it

Claims (6)

1. a kind of accurate prediction technique of direct-drive high-speed feed system kinematic accuracy for considering mechanical twisting oscillation, which is characterized in that The following steps are included:

Step 1 obtains mechanical system according to the direct-drive high-speed feed system kinematic accuracy analysis model for considering mechanical twisting oscillation It unites the disturbance transfer functions of three direction torsional oscillations；

Step 2, the disturbance transfer 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, the differentiation in system interference transmission function and step 3 obtained using step 1 is as a result, obtain considering mechanical The system motion precision of torsional oscillation.

2. a kind of direct-drive high-speed feed system kinematic accuracy for considering mechanical twisting oscillation according to claim 1 is accurately pre- Survey method, which is characterized in that in step 1, the expression formula of the disturbance transfer function of three direction torsional oscillations of mechanical system are as follows:

Wherein, G_rp(s), G_ry(s) and G_rrIt (s) is respectively mechanical vertical dip mining, beat oscillation and roll oscillation interference transmitting letter Number.

3. a kind of direct-drive high-speed feed system kinematic accuracy for considering mechanical twisting oscillation according to claim 1 is accurately pre- Survey method, which is characterized in that in step 2, the expression formula of characteristic equation are as follows:

Wherein, a_p=T_vJ_y；a_y=T_vJ_z；a_r=T_vJ_x；b_p=T_vC_θy+K_vK_FT_vM_pS_p；b_y=T_vC_θz+K_vK_FT_vM_yS_y；b_r=T_vC_θx+ K_vK_FT_vM_rS_r；c_p=T_vK_θy+K_vK_FM_pS_p+K_pK_vK_FT_vM_pS_p；d_p=K_pK_vK_FT_vM_pS_p；c_y=T_vK_θz+K_vK_FM_yS_y+ K_pK_vK_FT_vM_yS_y；d_y=K_pK_vK_FT_vM_yS_y；

c_r=T_vK_θx+K_vK_FM_rS_r+K_pK_vK_FT_vM_rS_r；d_r=K_pK_vK_FT_vM_rS_r。

4. a kind of direct-drive high-speed feed system kinematic accuracy for considering mechanical twisting oscillation according to claim 1 is accurately pre- Survey method, which is characterized in that in step 3, the specific method differentiated to the root of characteristic equation is:

WhenWhen, characteristic equation has a real root and two conjugation imaginary roots；

WhenAndWhen, characteristic equation has a real root and two conjugate radicals Root；

WhenAndWhen, there are three real roots for characteristic equation；I=p, y, r.

5. a kind of direct-drive high-speed feed system kinematic accuracy for considering mechanical twisting oscillation according to claim 1 is accurately pre- Survey method, which is characterized in that in step 4, consider the expression formula of the system motion precision of mechanical twisting oscillation:

x_m0(t)=x_Σtrp0(t)+x_Σtry0(t)+x_Σtrr0(t)

Wherein, x_Σtrp0(t)、x_Σtry0(t) and x_Σtrr0It (t) is respectively that mechanical pitch vibration, beat oscillation and roll oscillation are made At system motion output response.

6. a kind of direct-drive high-speed feed system kinematic accuracy for considering mechanical twisting oscillation according to claim 1 is accurately pre- Survey method, which is characterized in that in step 4, the differentiation knot in system interference transmission function and step 3 that is obtained using step 1 Fruit obtains the system motion precision for considering mechanical twisting oscillation, and specific method is:

The system interference transmission function obtained using step 1, obtains the kinematic accuracy under perturbation action under system complex field, leads to It crosses inverse Laplace transformation to handle the kinematic accuracy under system complex field under the perturbation action, and according in step 3 Differentiate as a result, obtaining considering the system motion precision of mechanical twisting oscillation.