Modeling method for friction of numerical control system and application thereof

Abstract

The application belongs to the technical field of dynamics analysis of numerical control system, and discloses a modeling method of friction of a numerical control system and application thereof, which comprises the following steps: dividing the friction into hysteresis friction and static friction, which are respectively used to describe dynamic characteristics and static characteristics of the friction; fitting the hysteresis friction at a speed close to zero by using a hysteresis curve, and degrading the hysteresis friction into Coulomb friction at a high speed stage to obtain a hysteresis friction model; degrading the static friction into zero at a speed close to zero, and fitting the static friction by using a Stribeck curve at a high speed stage to obtain a static friction model; and performing parameter identification on a friction model composed of the hysteresis friction model and the static friction model to obtain an optimal friction model. The application solves the technical problems that the following effect is poor and the following error is large at a speed close to zero and a speed reverse of the numerical control system.

Description

Technical Field

[0001] This invention belongs to the technical field of CNC system dynamics analysis, and more specifically, relates to a modeling method for frictional forces in CNC systems and its application. Background Technology

[0002] With the continuous development of the manufacturing industry, machined parts are becoming increasingly precise and complex, requiring CNC systems to achieve higher precision in their tracking performance. The tracking performance of a CNC system refers to the error between the actual running position and the commanded running position. Friction, as a nonlinear physical phenomenon generated between contact surfaces in relative motion, has a significant impact on the tracking performance of CNC systems, especially the low-speed crawling phenomenon that occurs when the CNC system is running at low speeds and the sudden increase in tracking error at the reversal point when the speed reverses. Therefore, to improve the tracking performance of a CNC system, it is necessary to reduce or eliminate the influence of friction, and an accurate mathematical model of friction is a prerequisite for suppressing or even eliminating the influence of friction.

[0003] Patent CN112462611A discloses a friction model based on a fractional-order model, which describes the friction hysteresis curve. However, the fractional-order model has a large computational load, which will lead to a large computational consumption in parameter identification and engineering applications.

[0004] Patent CN109940609B discloses a friction model based on a centrosymmetric static friction model. This invention divides motion into four operating states by velocity and acceleration, and each state is described by a static friction model with different friction parameters, thereby describing the hysteresis characteristics of friction. This state division not only multiplies the friction model parameters, but also requires additional state division steps in practical applications, resulting in a large computational load. Furthermore, in the viscous friction stage, the four different models have different descriptions due to their different parameters, leading to different descriptions of static characteristics, thus failing to accurately describe the static friction characteristics.

[0005] Zhang Xingang et al. proposed a Bouc-Wen hysteresis curve to describe the dynamic characteristics of friction. Compared with classical dynamic friction models such as the LuGre friction model, the Bouc-Wen hysteresis curve has more parameters to control the curve shape and can better describe the characteristics of friction in the pre-sliding stage. However, existing hysteresis curve models default to zero initial values ​​when solving the differential equation of the hysteresis curve. In actual working conditions, the friction force before the CNC feed servo system starts is not zero, and different working conditions have different initial friction force values. At the same time, the parameter identification strategy of existing hysteresis friction models uses one-time parameter identification for static and dynamic parameters, which involves a large number of parameters, an uncertain search range, and high computational cost for parameter identification. Summary of the Invention

[0006] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a modeling method for friction force in CNC system and its application, so as to solve the technical problems of poor following effect and large following error in CNC system at near-zero speed and reverse speed.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for modeling frictional forces in a CNC system is provided, the method comprising the following steps:

[0008] Friction is divided into hysteretic friction and static friction, which are used to describe the dynamic and static characteristics of friction, respectively.

[0009] Hysteretic friction is fitted using a hysteresis curve when the speed is near zero, and degenerates into Coulomb friction at high speed, thus obtaining a hysteretic friction model; wherein, when the speed of the CNC system is greater than the speed threshold, the CNC system is in the high-speed stage.

[0010] Static friction degenerates to zero near the zero velocity. At high speeds, the static friction model is obtained by fitting the Stribeck curve.

[0011] The parameters of the friction model composed of the hysteretic friction model and the static friction model are identified to obtain the optimal friction model.

[0012] The friction model is as follows:

[0013]

[0014] In the formula, F bw For hysteretic friction, F sc For static friction, F s For static friction, F c For Coulomb friction, v s Let B be the Stribeck velocity, B be the viscous friction coefficient, ξ be the equivalent bristle deformation, ρ, σ, and n be the hysteresis curve shape control coefficients, and F be the hysteresis velocity. begin F is the initial frictional force when the CNC system starts up. f ρ is the overall frictional force predicted by the model; v is the speed of the CNC system.

[0015] Furthermore, the range of values ​​for the coefficient σ controlling the hysteresis curve is: 0 < σ < 1.

[0016] Furthermore, through parameter F begin To describe the initial frictional force under different working conditions, F is calculated using current data. begin The value of .

[0017] Furthermore, the speed threshold is 360 mm / min.

[0018] Furthermore, based on the curve characteristics and physical parameter relationships of the friction force-velocity curve, the parameters of the friction model composed of the hysteretic friction force model and the static friction force model are identified.

[0019] Furthermore, the frictional forces corresponding to different speeds during the motion of the CNC system are collected. The frictional force-velocity relationship curve is composed of different speeds and their corresponding frictional forces. The features of the parameters in the frictional model are extracted from the frictional force-velocity relationship curve. The extracted features are used to obtain the precise values ​​of some parameters and the range of other parameters. Then, the parameters within the determined range are iteratively optimized through optimization algorithms to obtain their precise values.

[0020] Furthermore, the extracted features include curve features and physical parameter relationships on the friction-velocity relationship curve. Curve features include the slope corresponding to the intersection of the friction-velocity relationship curve with the horizontal axis and the first point of the hysteresis curve where the velocities corresponding to different friction forces are sufficiently close. Physical parameter relationships include: static friction Fs is 1.1-5 times the Coulomb friction Fc, σ is in the range of (0,1), and n is in the range of (1,20).

[0021] Furthermore, parameter F c The precise value of parameter F is determined by the corresponding characteristics of the friction force-velocity relationship curve, along with B. s Through F c The precise value determines the range of values ​​for parameter v. s The range of values ​​for ρ is determined by extracting the characteristics of the parameters in the friction model from the friction force-velocity relationship curve, while the values ​​of parameters σ and n are selected empirically.

[0022] Furthermore, data from the high-speed phase of the friction-velocity relationship curve are selected, at which point the hysteresis curve degenerates into a friction model with a viscous damping term:

[0023] F f =F c +Bv

[0024] The parameter F is determined using the least squares method. c and B;

[0025] The velocity corresponding to the first point in the friction-velocity relationship curve that enters the static region is selected as v. s The left boundary is used to calculate the average slope of Fv using a sliding window. The velocity corresponding to the point where the slope is sufficiently close to B is taken as v. s The right boundary; select the intersection point of the friction force-velocity relationship curve with the horizontal axis, and use the characteristic slope k, velocity v and acceleration a of the intersection point to calculate ρ.

[0026] The present invention also provides a compensation method based on a friction model, which includes the following steps: First, a friction model is constructed using the modeling method for friction force of a CNC system as described above, and the friction force is obtained by simulating different speeds during the operation of the CNC system using the friction model; then, a compensator is used to calculate the current based on the friction force obtained by the friction model simulation and the actual speed of the CNC system, and then the current is used to feedforward the CNC servo feed system.

[0027] In summary, compared with the prior art, the modeling method for frictional force in CNC systems and its application provided by this invention have the following advantages:

[0028] 1. By setting an initial friction force, the hysteresis curve model can be better adapted to different machine tool start-up states. This invention adds an initial friction force term for the motion of CNC servo feed system in different start-up and reverse states. The initial friction force is used to adapt to the changes in different working conditions and to identify parameters to obtain a friction model. This solves the problem that the existing hysteresis friction model is not effective in the near-zero speed stage and reverse segment.

[0029] 2. This invention proposes a parameter identification method based on the feature extraction of friction force-velocity curve parameters, which reduces the number of parameters to be identified, narrows the parameter search range, and improves the efficiency of model parameter identification. This invention analyzes the parameter features of the friction model, extracts the parameter features of the corresponding parameters from the friction force-velocity diagram, and quickly obtains the accurate values ​​or value ranges of the friction parameters, thereby reducing the number of parameters that the optimization algorithm needs to identify and narrowing the search space, thus reducing the amount of computation and time required to identify friction parameters.

[0030] 3. This invention models the friction force of the CNC servo feed system and determines the parameters through an efficient parameter identification algorithm. Furthermore, it performs feedforward compensation based on the friction force, which can reduce the following error of the servo feed system and improve the system's following performance. Attached Figure Description

[0031] Figure 1 This is a flowchart of a method for modeling frictional forces in a CNC system provided by the present invention;

[0032] Figure 2 This is a schematic diagram of the machine tool CNC servo feed system performing "triangular wave" motion speed command signal according to an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram of the friction force-speed range of the CNC feed system provided in the embodiment of the present invention at different feed speeds;

[0034] Figure 4This is a schematic diagram of the friction parameter identification principle provided in an embodiment of the present invention;

[0035] Figure 5 This is a schematic diagram illustrating the effect of using the Lugre model to compensate the CNC servo feed system, as provided in an embodiment of the present invention.

[0036] Figure 6 This is a schematic diagram illustrating the effect of compensating the data servo feed system using the original hysteresis curve model, as provided in an embodiment of the present invention.

[0037] Figure 7 This is a schematic diagram illustrating the effect of the hysteresis curve model provided in this embodiment of the invention after compensating the CNC feed system. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be 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 illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0039] Please see Figure 1 and Figure 2 This invention provides a modeling method for friction in CNC systems. The method can construct a simple mathematical form of hysteretic friction model applicable to different working conditions, and use an efficient identification strategy to identify parameters, thereby obtaining a more universal hysteretic friction model that is easy to use in engineering.

[0040] The method mainly includes the following steps:

[0041] Friction is divided into hysteretic friction and static friction, which are used to describe the dynamic and static characteristics of friction, respectively.

[0042] Hysteretic friction is fitted using a hysteresis curve when the speed is near zero, and degenerates into Coulomb friction at high speed, thus obtaining a hysteretic friction model; wherein, when the speed of the CNC system is greater than the speed threshold, the CNC system is in the high-speed stage.

[0043] Static friction degenerates to zero near the zero velocity. At high speeds, the static friction model is obtained by fitting the Stribeck curve.

[0044] The parameters of the friction model composed of the hysteretic friction model and the static friction model are identified to obtain the optimal friction model.

[0045] The friction model is as follows:

[0046]

[0047] In the formula, F bw For hysteretic friction, F sc For static friction, F s For static friction, F c For Coulomb friction, v s Let B be the Stribeck velocity, B be the viscous friction coefficient, ξ be the equivalent bristle deformation, ρ, σ, and n be the hysteresis curve shape control coefficients, and F be the hysteresis velocity. begin F is the initial frictional force when the CNC system starts up. f ρ is the overall frictional force predicted by the model; v is the speed of the CNC system.

[0048] The coefficient σ controlling the hysteresis curve has the following range: 0 < σ < 1; this is achieved through parameter F. begin To describe the initial frictional force under different operating conditions, data with speeds near zero at the beginning of the test cases are selected, and F is calculated using current data. begin The precise value.

[0049] Specifically, a speed threshold is set. When the speed of the CNC system is between the speed zero point and the speed threshold, the CNC system is in the low-speed stage; when the speed of the CNC system is greater than the speed threshold, the CNC system is in the high-speed stage. More accurately, the low-speed and high-speed stages are nonlinear and linear stages, respectively. Nonlinear characteristics are more pronounced at low speeds, hence the term "low-speed stage," while linearity is more pronounced at high speeds, hence the term "high-speed stage." The high-speed and low-speed stages are mainly distinguished based on the compensation results of speed acceleration. After adding speed acceleration feedforward, the following error will be larger in the nonlinear stage and smaller in the linear stage. The magnitude of the following error under speed acceleration can be used to determine whether it is a nonlinear or linear stage. The speed threshold is 360 mm / min.

[0050] Hysteresis friction describes the dynamic characteristics of friction when the speed is near zero, while static friction does not describe the characteristics of friction when the speed is near zero and is defined as zero when the speed is near zero.

[0051] For the aforementioned friction model, this embodiment employs a parameter identification method that optimizes parameter ranges based on the curve characteristics of the friction force-velocity curve and the relationship between physical parameters. Specifically, the friction forces corresponding to different speeds during the motion of the CNC system are collected. Different speeds and their corresponding friction forces form a friction force-velocity relationship curve. Features of the parameters in the friction model are extracted from this curve. These features are used to obtain the precise values ​​of certain parameters and the ranges of the remaining parameters. Then, an optimization algorithm iteratively optimizes the parameters within the determined range to obtain their precise values. These features primarily include the curve characteristics of the friction force-velocity relationship curve and the relationship between physical parameters.

[0052] Curve characteristics: the slope corresponding to the intersection of the friction-velocity relationship curve and the horizontal axis, the slope of the long side of the checkmark curve, the lowest point of the checkmark curve, and the first point on the hysteresis curve where the velocities corresponding to different friction forces are sufficiently close.

[0053] Physical parameter relationships: static friction force Fs is 1.1-5 times that of Coulomb friction force Fc, σ ranges between (0,1), and n ranges between (1,20).

[0054] Parameter F c The precise value of B is determined using the corresponding characteristics of the friction force-velocity relationship curve. Parameter F s Through F c The precise value determines the range of values ​​for parameter v. s The range of values ​​for ρ is determined by extracting the characteristics of the parameters in the friction model from the friction force-velocity relationship curve, while the values ​​of parameters σ and n are selected empirically.

[0055] Data from the high-speed phase of the friction-velocity relationship curve are selected, at which point the hysteresis curve degenerates into a friction model with a viscous damping term:

[0056] F f =F c +Bv

[0057] The parameter F is determined using the least squares method. c and B; F s The value range is defined as [1.1F]. c 5F c ].

[0058] The velocity corresponding to the first point in the friction-velocity relationship curve that enters the static region is selected as v. s The left boundary is used to calculate the average slope of Fv using a sliding window. The velocity corresponding to the point where the slope is sufficiently close to B is taken as v. s The right boundary.

[0059] Select the intersection point of the friction-velocity relationship curve with the horizontal axis, and calculate ρ using the characteristic slope k, velocity v, and acceleration a at that intersection point. Select the range of σ as [1e...]. -3 [0.9]; the range of n is selected as [1 / 3, 20]. For parameters whose range is only determined, an optimization algorithm is used to identify them, and the search space is the search space obtained above.

[0060] The present invention also provides a compensation method based on a friction model, the method comprising the following steps: First, a friction model is constructed using the friction modeling method of the CNC system as described above, and the friction force is obtained by simulating the friction force at different speeds during the operation of the CNC system using the friction model; then, a compensator is used to calculate the current based on the friction force obtained by the friction model simulation and the actual speed of the CNC system, and then the current is used to feedforward the CNC servo feed system.

[0061] Based on the hysteretic friction model, this invention identifies parameters for the friction state of a CNC servo feed system to obtain a single-axis friction model of the machine tool servo feed system.

[0062] (1) Collect friction force data of a single axis of the machine tool under the "triangular wave" speed command.

[0063] The motor load current is directly proportional to the load torque. When the machine tool servo feed system operates in a triangular wave pattern, the load torque is approximately equal to the sum of the frictional torque and the inertial torque. The inertial torque can be obtained by measuring the acceleration of a single axis, and the load torque can be obtained by measuring the load current. The frictional torque can be indirectly obtained from these two measurements. The triangular wave speed commands for each axis of the machine tool are as follows: Figure 2 As shown, by performing reciprocating uniformly accelerated motion with different accelerations, and combining the load current and acceleration, the magnitude of friction experienced by the current axis can be obtained. Therefore, the curve of friction force on a single machine tool axis as a function of speed can be obtained as shown below. Figure 3 As shown.

[0064] (2) Identify friction forces on each axis based on friction force and velocity data

[0065] Based on the established friction model and the data collected in (1), a friction-velocity relationship curve showing the change of friction force with velocity is plotted. The corresponding friction parameters can be obtained using parameter feature extraction and optimization algorithms. The identification principle is as follows: Figure 4 As shown. Data from the test cases with speeds near zero at the beginning of the test time was selected, and F was calculated using the current data. beginThe precise value of the static friction and viscous friction coefficient is determined by selecting high-speed data from the friction-velocity relationship curve and using the least squares method. The slope of the intersection of the friction-velocity relationship curve with the horizontal axis and the corresponding velocity acceleration are used to determine ρ. The range of Coulomb friction is determined using static friction. Starting from zero velocity, the friction-velocity relationship curve is used to find the first velocity where the corresponding two different friction forces are sufficiently close; this velocity is taken as the left boundary of the Stribeck velocity. Using a fixed-length sliding window, the average slope is calculated from the data within the window. When the calculated slope is sufficiently close to the identified viscous friction coefficient, the corresponding velocity is taken as the right boundary of the Stribeck velocity. Thus, the range of the Stribeck velocity is determined. The range of σ is defined as [1e...]. -3 The range of n is defined as [1 / 3, 20]. The Coulomb friction force, Stribeck velocity, σ, and n in the friction model are used as objective parameters; the corresponding value range of each parameter is used as the search space; an intelligent optimization algorithm (genetic algorithm) is used to minimize the deviation between the simulated friction force output by the friction model and the measured friction force, continuously updating the parameters output by the friction model, and finally obtaining the identification results of the friction model parameters. When the iteration count of the intelligent optimization algorithm reaches the upper limit and the obtained optimal parameters meet the requirements, the friction model is constructed using the optimal parameters.

[0066] The intelligent optimization algorithm is a genetic algorithm, particle swarm optimization algorithm, differential evolution algorithm, simulated degradation algorithm, particle swarm algorithm based on Gaussian sampling, firework algorithm, or neural network algorithm.

[0067] Compared with previous identification algorithms, the identification algorithm of this invention reduces the number of parameters to be identified, narrows the search space for parameters, and has a faster identification speed. Each identification can be completed within a few minutes, which is convenient for comparative experiments.

[0068] (3) Use the constructed model for feedforward control

[0069] The simulated friction force output by the friction model is converted into current, and current feedforward control is performed on the CNC servo feed system. Figure 5 This is the effect after compensating the CNC servo feed system using the Lugre friction model. Figure 6 This is a schematic diagram illustrating the effect of compensating the CNC servo feed system using the original hysteresis curve model, as provided in an embodiment of the present invention. Figure 7 This is a schematic diagram illustrating the effect of compensating a CNC servo feed system using an improved hysteresis curve model, as provided in an embodiment of the present invention. It can be seen that the hysteresis curve friction model provided by the present invention exhibits better performance than the original hysteresis curve model.

[0070] Those skilled in the art will readily understand 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 within the scope of protection of the present invention.

Claims

1. A method for modeling frictional forces in a numerical control system, characterized in that, The method includes the following steps: Friction is divided into hysteretic friction and static friction, which are used to describe the dynamic and static characteristics of friction, respectively. Hysteretic friction is fitted using a hysteresis curve when the speed is near zero, and degenerates into Coulomb friction at high speed, thus obtaining a hysteretic friction model; wherein, when the speed of the CNC system is greater than the speed threshold, the CNC system is in the high-speed stage. Static friction degenerates to zero near the zero velocity. At high speeds, the static friction model is obtained by fitting the Stribeck curve. The parameters of the friction model composed of the hysteretic friction model and the static friction model are identified to obtain the optimal friction model. The friction model is as follows: In the formula, This is hysteretic friction. It is static friction. For static friction, For Coulomb friction, For Stribeck speed, The coefficient of viscous friction, For equivalent bristle deformation, This is the hysteresis curve shape control coefficient. This refers to the initial frictional force when the CNC system starts up. The overall frictional force predicted by the model; For the speed of the CNC system; Through parameters To describe the initial frictional force under different working conditions, and to calculate it using current data. The values ​​are determined; based on the curve characteristics and physical parameter relationships of the friction force-velocity relationship curve, the parameters of the friction model composed of the hysteretic friction force model and the static friction force model are identified; the friction force corresponding to different speeds during the motion of the CNC system is collected, and the friction force-velocity relationship curve is composed of different speeds and their corresponding friction forces. The features of the parameters in the friction model are extracted from the friction force-velocity relationship curve. The extracted features are used to obtain the precise values ​​of some parameters and the range of other parameters. Then, the parameters within the determined range are iteratively optimized through an optimization algorithm to obtain their precise values.

2. The method for modeling friction in a CNC system as described in claim 1, characterized in that: The coefficient of the control hysteresis curve The range of values ​​for is: .

3. The method for modeling friction in a CNC system as described in claim 1, characterized in that: The speed threshold is 360 mm / min.

4. The method for modeling friction in a CNC system as described in claim 1, characterized in that: The extracted features include curve features on the friction-velocity relationship curve and physical parameter relationships. These physical parameter relationships include: static friction Fs is 1.1-5 times the Coulomb friction Fc. The range of is between (0,1) and the range of n is between (1,20).

5. The method for modeling frictional forces in a CNC system as described in any one of claims 1-4, characterized in that: parameter and The precise values ​​of the parameters are determined by the corresponding characteristics of the friction force-velocity relationship curve. pass The precise value determines the range of values ​​for the parameter. and The range of values ​​for the parameters is determined by extracting features from the friction force-velocity relationship curve of the friction model. and The parameter values ​​are selected based on experience.

6. The method for modeling friction in a CNC system as described in claim 1, characterized in that: Data from the high-speed phase of the friction-velocity relationship curve are selected, at which point the hysteresis curve degenerates into a friction model with a viscous damping term: Parameters are determined using the least squares method. and ; The velocity corresponding to the first point in the friction-velocity relationship curve that enters the static region is selected as... The left boundary is used to calculate the average slope of Fv using a sliding window; the intersection point of the friction-velocity relationship curve and the horizontal axis is selected, and the characteristic slope of this intersection point is used. ,speed and acceleration Calculate .

7. A compensation method based on a friction model, characterized in that, The method includes the following steps: First, a friction model is constructed using the modeling method for friction force of a CNC system as described in any one of claims 1-6, and the friction force is obtained by simulating different speeds during the operation of the CNC system using the friction model; then, a compensator is used to calculate the current based on the friction force obtained by the friction model simulation and the actual speed of the CNC system, and then the current is used to feedforward the CNC servo feed system.

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