A friction compensation method and system suitable for CNC machine tools

Abstract

The present invention belongs to the technical field related to numerical control systems and discloses a friction compensation method and system suitable for numerically controlled machine tools. The method includes the following steps: constructing a single-state variable friction model; obtaining command position signals for the current control cycle and the previous control cycle in real time, calculating the command speed for the current cycle using the command position signal, and solving the predicted friction force for the current control cycle using the command speed and the single-state variable friction model; constructing a relationship between the predicted friction force and the current feedforward amount, calculating the current feedforward amount for the current control cycle using the relationship and the predicted friction force for the current control cycle obtained, and compensating the current feedforward amount to the current control unit of the current control cycle of the numerical control system to be processed, thereby achieving friction compensation. The present invention facilitates modeling, and the friction model is more capable of fitting the friction characteristics at the reverse direction, resulting in a better compensation effect.

Description

Technical Field

[0001] The present invention belongs to the technical field related to numerical control systems, and more specifically, relates to a friction compensation method and system suitable for numerically controlled machine tools. Background Art

[0002] CNC machine tools offer the advantages of high machining precision and stable machining quality. However, friction plays a crucial role in high-precision servo mechanism position control and low-speed control during machining, hindering system performance. Not only does it create dead zones or limit cycles in position servo mode, leading to steady-state errors, but it can also cause creep and oscillation in velocity servo mode, and even cause the system to enter a chaotic state of disordered motion, significantly degrading performance. In actual machining, using inaccurate friction models for compensation often results in machining defects such as cross-quadrant cuts and horizontal machined streaks. Therefore, establishing accurate friction forces and implementing friction compensation are important research topics.

[0003] The study of friction has a history of hundreds of years, and friction models can be divided into static models and dynamic models. As a static model, the Stribeck friction model has a simple expression and can well fit the friction characteristics of the low-speed range, making it widely used in industry. However, the Stribeck friction model fails to reflect the friction characteristics during speed reversal. When using Stribeck friction for compensation, the following error in the speed reversal range is large (following error is command position minus actual position). As a dynamic model, the Lugre friction model first introduces a state variable z, which can to some extent reflect the friction characteristics of the reversal range (the process of speed decreasing from low speed to zero and then accelerating in the reverse direction). However, this also increases the difficulty of modeling, and the initial value of the state variable z during the compensation process affects the compensation effect. As a dynamic model, the GMS friction model better fits the friction force, but its structure is complex, modeling is difficult, and calculating the compensation amount using this model is time-consuming. Therefore, a friction compensation method that can solve the above problems is needed. Summary of the Invention

[0004] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a friction compensation method and system suitable for CNC machine tools to solve the problem of large following error during machining of traditional CNC machine tools.

[0005] To achieve the above object, according to one aspect of the present invention, a friction compensation method applicable to a CNC machine tool is provided, the method comprising the following steps:

[0006] Obtaining physical parameters of the CNC system to be processed, and using the physical parameters to construct a single-state variable friction model;

[0007] Acquire command position signals of the current control cycle and the previous control cycle in real time, calculate the command speed of the current cycle using the command position signals, and solve the predicted friction force of the current control cycle using the command speed and a single-state variable friction model;

[0008] A relationship between the predicted friction force and the current feedforward is constructed, and the current feedforward of the current control cycle is calculated using the relationship and the predicted friction force of the current control cycle obtained by solving the problem. The current feedforward is then compensated to the current control unit of the current control cycle of the CNC system to be processed, thereby achieving friction compensation.

[0009] Further preferably, the relationship of the single state variable friction model is as follows:

[0010]

[0011] Among them, F sc is the static friction, F bw is the dynamic friction force, Fs is the maximum static friction force, Fc is the Coulomb friction force, v s is the Stribeck velocity, B is the viscous friction coefficient, ρ is the pre-slip bristle stiffness, which is used to control the slope of the hysteresis loop, σ is the pre-slip length coefficient, which is used to adjust the shape of the hysteresis loop and control the length of the displacement in the pre-slip stage, and n is the smoothness of the pre-slip stage, which is used to control the smoothness of the transition curve from the pre-slip stage to the macro-slip stage.

[0012] Further preferably, the predicted friction force of the current control cycle is solved according to the following steps:

[0013] Discretizing the relationship between the bristle shape variables in the single-state variable friction model, substituting the command speed of the current control cycle into the discretized relationship between the bristle shape variables to calculate the bristle shape variables of the current control cycle;

[0014] The bristle shape variable of the current control cycle is substituted into the single-state variable friction model to calculate and obtain the predicted friction force of the current control cycle.

[0015] Further preferably, the bristle shape variable of the current control cycle is calculated according to the following relationship:

[0016] ξ i (k)=ρ(1-(σ+(1-σ)sign(v i (k-1)ξ i (k-1))|ξ i (k-1)| n )v i (k-1)ΔT+ξ i (k-1)

[0017] Among them, ξ i (k) is the bristle deformation of the control period k, ρ is the pre-slip bristle stiffness, σ is the pre-slip length coefficient, v i (k-1) is the command speed of control cycle k-1, ξ i (k-1) is the bristle shape variable of control cycle k-1, n is the smoothness of the pre-sliding stage, and ΔT is the interpolation period of the CNC machine tool.

[0018] Further preferably, the value of the bristle shape variable in the current control cycle is as follows:

[0019]

[0020] Among them, ξ i (k) is the bristle shape variable of control period k.

[0021] Further preferably, the command speed of the current control cycle is calculated according to the following relationship:

[0022]

[0023] Among them, v i (k) is the command speed of the current control cycle k, s i (k) is the command position signal of the current control cycle k, s i (k-1) is the command position signal of the current control cycle k-1, and ΔT is the interpolation cycle of the CNC machine tool.

[0024] Further preferably, the calculation relationship between the bristle deformation amount, the command speed and the initial value of the predicted friction force is as follows:

[0025]

[0026] F fi (0) = F s ξ i (0)

[0027] v i (0)=0

[0028] Among them, ξ i (0) is the initial value of the bristle shape variable, F fi (0) is the initial value of the predicted friction force, v i (0) is the initial value of the command speed, k t is the torque constant, F s is the maximum static friction, I init is the load current in the initial transition state.

[0029] Further preferably, the relationship between the predicted friction force and the current feedforward amount is as follows:

[0030]

[0031] Among them, IF fi (k) is the friction compensation amount, h is the lead of the screw nut structure of the CNC machine tool, P is the feedforward resolution in the servo drive, k t is the torque constant.

[0032] Further preferably, the physical parameters include system parameters, mechanical parameters, motor parameters and servo parameters, the system parameters are the interpolation period, the mechanical parameters include maximum static friction, Coulomb friction, Stribeck speed, viscous friction, bristle stiffness, pre-slip length coefficient, pre-slip smoothness and lead of the machine tool, the motor parameters are the motor torque constant, and the servo parameters are the current feedforward resolution.

[0033] According to another aspect of the present invention, a friction compensation system applicable to a CNC machine tool is provided. The system includes an actuator for executing the above-mentioned friction compensation method applicable to a CNC machine tool.

[0034] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0035] 1. This invention uses a single-state variable friction model to predict the friction force of the current control cycle, then converts the predicted friction force into a current feedforward value. Finally, the current feedforward value is compensated into the current loop, thereby improving the response characteristics of the current loop and reducing the following error during CNC machine tool processing.

[0036] 2. The single-state variable friction model established by the present invention is provided with a bristle deformation variable relationship formula with friction hysteresis characteristics. The reverse part of the CNC machine tool is mainly a pre-sliding stage, and the friction characteristics of the pre-sliding stage are mainly friction hysteresis characteristics. The bristle deformation variable relationship formula provided by the present invention very accurately describes the friction hysteresis characteristics. Compared with the existing CNC machine tool feed system friction compensation method, it can more accurately fit the friction characteristics of the reverse part and has a better compensation effect. It can be used to reduce the following error in the reverse section, thereby improving the motion accuracy of the CNC machine tool. It can make high-precision predictions of the friction characteristics of low-speed reverse. In addition, compared with the existing single-state friction model, the speed overshoot and speed lag terms that have a smaller impact on the following error are discarded, and it is also easier to model.

[0037] 3. When solving the predicted friction force, the present invention discretizes the continuous model of the bristle shape variable and then calculates it. It takes into account the inconsistency of the forward and reverse speed parameters and subdivides the feedforward quantity to ensure that the feedforward quantity does not produce large mutations. This is also of reference value for other error compensation such as thrust fluctuation.

[0038] 4. The present invention limits the value of the bristle deformation, ensuring a smooth transition from the pre-sliding stage to the sliding stage and improving the stability of friction compensation;

[0039] 5. Compared with the existing CNC machine tool feed system friction compensation method, the feed system friction compensation method based on the improved SSV model of the present invention processes the initial conditions of the model, can effectively fit the characteristics of the starting section, and thus reduce the following error of the starting section. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 1 is a flow chart of a friction compensation method for a feed system based on an improved SSV model constructed according to a preferred embodiment of the present invention;

[0041] Figure 2 1 is a schematic diagram of a friction compensation method for a feed system based on an improved SSV model constructed in accordance with a preferred embodiment of the present invention;

[0042] Figure 3 Schematic diagram of the command signal required for feedforward calculation constructed according to the preferred embodiment of the present invention;

[0043] Figure 4 It is a comparison diagram of position following error between the improved SSV friction feedforward compensation constructed according to the preferred embodiment of the present invention and the speed acceleration feedforward compensation with only the speed acceleration feedforward compensation turned on. DETAILED DESCRIPTION

[0044] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0045] like Figure 1 As shown, a friction compensation method suitable for CNC machine tools specifically includes:

[0046] (1) Obtain the CNC system parameters, servo parameters and SSV friction parameters identified by SSTT friction parameters. The parameters are shown in Table 1. The friction force is divided into two parts: static friction force F sc , dynamic friction F bw , where F sc It reflects the Stribeck effect and can well fit the friction characteristics of the low-speed section, while the dynamic friction force F bw It reflects the friction hysteresis characteristics of the reverse section, where ξ is the bristle deformation.

[0047] Table 1 Relevant parameters required for friction feedforward

[0048]

[0049]

[0050] The single state variable (SSV) friction model based on Bouc-Wen is as follows:

[0051]

[0052] The present invention first improves the above formula (1) to remove the friction hysteresis term that affects the motion accuracy. and velocity overshoot The SSV friction model is simplified into the following formula:

[0053]

[0054] Among them, F sc is the static friction, F bw is the dynamic friction force, Fs is the maximum static friction force, Fc is the Coulomb friction force, v s is the Stribeck velocity, B is the viscous friction coefficient, which is the correlation between friction and lubrication viscosity. The three friction hysteresis control parameters ρ, σ, and n jointly control the friction hysteresis loop. ρ is the pre-slip bristle stiffness, which is used to control the slope of the hysteresis loop. σ is the pre-slip length coefficient, which is used to adjust the shape of the hysteresis loop and control the length of the pre-slip stage displacement. n is the smoothness of the pre-slip stage, which is used to control the smoothness of the transition curve from the pre-slip stage to the macro-slip stage.

[0055] The friction force is theoretically predicted based on the above formula, and converted into current compensation value to compensate the current loop to realize friction compensation of CNC machine tools.

[0056] (2) When the machine tool is in the cycle start phase, obtain the load current value I of the first interpolation cycle init , calculate the initial bristle shape variable ξ i (0), initial velocity v i (0), initial predicted friction force F fi (0).

[0057] The calculation formula is as follows

[0058]

[0059] F fi (0) = F s ξ i (0)

[0060] v i (0)=0

[0061] Among them, ξ i (0) is the initial value of the bristle shape variable, F fi (0) is the initial value of the predicted friction force, v i (0) is the initial value of the command speed, k t is the torque constant, which is the ratio of rated current to rated torque, F s is the maximum static friction, I init is the load current in the initial transition state.

[0062] (3) The CNC system obtains the command position signal s in the current control cycle in real time i (k) and the position information s of the last interpolation cycle i (k-1), and calculate the current command speed v i (k), calculate the current bristle shape variable ξ based on the speed of the previous cycle i (k), and then obtain the predicted friction force F fi (k).

[0063]

[0064] ξ i (k)=ρ(1-(σ+(1-σ)sign(v i (k-1)ξ i (k-1))|ξ i (k-1)| n )v i (k-1)ΔT+ξ i (k-1)

[0065] Limit the bristle shape variable to a maximum value of 1. When the speed is not reversed, only F is calculated. sc (k) Optimize friction compensation calculation time.

[0066]

[0067] F fi (k) = F s ·ξ i (k)+F sc

[0068] (4) The predicted friction force is converted into a current feedforward quantity, the current feedforward resolution of the drive is adapted and added to its current loop.

[0069]

[0070] Among them, IF fi(k) is the friction compensation amount, h is the lead of the screw nut structure of the CNC machine tool, which means the distance the worktable moves linearly when the rotary motor rotates one circle. P is the feedforward resolution in the servo drive, k t is the torque constant.

[0071] Steps (3) and (4) are the improved SSV friction feedforward implementation process for one control cycle, as shown in Figure 2 As shown in FIG, through the above-mentioned friction feedforward control process, the position following error in the starting segment and the reverse segment can be effectively reduced.

[0072] like Figure 3 As shown in FIG, this is a test speed signal for testing the compensation effect of the improved SSV friction compensation algorithm. An S-shaped speed curve is used, which is a commonly used processing curve.

[0073] like Figure 4 As shown in the figure, turning on friction compensation can effectively reduce the position following error in the reverse section. Compared with the effect of velocity acceleration feedforward compensation, the position following error can be reduced from 4.5μm to 1.8μm after turning on friction feedforward.

[0074] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A friction compensation method suitable for CNC machine tools, characterized in that: The method comprises the following steps: Obtaining physical parameters of the CNC system to be processed, and using the physical parameters to construct a single-state variable friction model; Acquire command position signals of the current control cycle and the previous control cycle in real time, calculate the command speed of the current cycle using the command position signals, and solve the predicted friction force of the current control cycle using the command speed and a single-state variable friction model; Constructing a relationship between the predicted friction force and the current feedforward amount, using this relationship and the predicted friction force of the current control cycle obtained by solving it to calculate the current feedforward amount of the current control cycle, and compensating this current feedforward amount to the current control unit of the current control cycle of the CNC system to be processed, thereby achieving friction compensation; The predicted friction force of the current control cycle is solved according to the following steps: Discretizing the relationship between the bristle shape variables in the single-state variable friction model, substituting the command speed of the current control cycle into the discretized relationship between the bristle shape variables to calculate the bristle shape variables of the current control cycle; The bristle shape variable of the current control cycle is substituted into the single-state variable friction model to calculate and obtain the predicted friction force of the current control cycle.

2. A friction compensation method for a CNC machine tool according to claim 1, characterized in that: The relationship of the single state variable friction model is as follows: in, is the static friction, is the dynamic friction force, Fs is the maximum static friction force, Fc is the Coulomb friction force, v s is the Stribeck velocity, B is the viscous friction coefficient, ρ is the pre-slip bristle stiffness, which is used to control the slope of the hysteresis loop, σ is the pre-slip length coefficient, which is used to adjust the shape of the hysteresis loop and control the length of the pre-slip stage displacement, and n It is the smoothness of the pre-sliding stage, which is used to control the smoothness of the transition curve from the pre-sliding stage to the macro-sliding stage.

3. The friction compensation method for a CNC machine tool according to claim 1, wherein: The bristle shape variable of the current control cycle is calculated according to the following relationship: in, is the bristle shape variable of control period k, is the pre-slip bristle stiffness, is the pre-slip length coefficient, is the instruction speed of control cycle k-1, is the bristle shape variable of the control period k-1, is the smoothness of the pre-slip stage, It is the interpolation cycle of CNC machine tools.

4. A friction compensation method for a CNC machine tool as claimed in claim 3, characterized in that: The values ​​of the bristle shape variables in the current control cycle are as follows: in, is the bristle shape variable of the control period k.

5. The friction compensation method for a CNC machine tool according to claim 1, wherein: The command speed of the current control cycle is calculated according to the following relationship: in, is the command speed of the current control cycle k, is the command position signal of the current control cycle k, is the command position signal of the current control cycle k-1, It is the interpolation cycle of CNC machine tools.

6. A friction compensation method for a CNC machine tool as claimed in claim 5, characterized in that: The calculation relationship between the bristle shape, command speed and initial value of predicted friction force is as follows: in, is the initial value of the bristle shape variable, is the initial value for the predicted friction, is the initial value of the command speed, is the torque constant, is the maximum static friction force, is the load current in the initial transition state.

7. The friction compensation method for a CNC machine tool according to claim 1, wherein: The relationship between the predicted friction force and the current feedforward is as follows: in, is the friction compensation amount, h is the lead of the screw nut structure of the CNC machine tool, P is the feedforward resolution in the servo drive, is the torque constant.

8. The friction compensation method for a CNC machine tool according to claim 1, wherein: The physical parameters include system parameters, mechanical parameters, motor parameters and servo parameters. The system parameters are the interpolation period. The mechanical parameters include the maximum static friction, Coulomb friction, Stribeck speed, viscous friction, bristle stiffness, pre-slip length coefficient, pre-slip smoothness and the lead of the machine tool. The motor parameters are the motor torque constant. The servo parameters are the current feedforward resolution.

9. A friction compensation system suitable for a CNC machine tool, characterized in that: The system includes an actuator for executing a friction compensation method applicable to a CNC machine tool as described in any one of claims 1 to 8.

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