A high-precision turning machining method, device and medium for non-circular contour parts in the position domain

Abstract

The present invention discloses a high-precision turning machining method, device and medium for non-circular contour parts, including: for the rotation system, a motor voltage excitation signal is given, the tool position output signal is collected, and the second-order state space model of the rotation system in the time domain is obtained by using the system identification toolbox; aiming at the problem that the change of the time period will significantly reduce the control performance of the rotation system, the definition of the position domain is given, and the time domain model of the rotation system is converted into the position domain model; according to the obtained position domain model, the position domain model is discretized and converted into a high-order full-drive model, and then the corresponding full-drive stabilizing controller is designed to stabilize the rotation system; the model predictive controller is designed to solve the optimal control law and inversely transform it into the full-drive control law through the corresponding relational expression. The present invention uses the full-drive system model to represent the rotation system in the position domain, which can not only maintain the physical interpretability of the model, but also avoid the bad matrix problems that often occur in traditional methods.

Description

Technical Field

[0001] The present invention relates to the field of precision machining, and particularly to a high-precision turning machining method, device and medium for non-circular contour parts in the position domain. Background Art

[0002] Numerical control machine tools play a crucial role in the machining of non-circular contour parts in fields such as automotive, marine, and aerospace. For example, components such as cams, camshafts, and convex elliptical pistons usually require high-precision turning to ensure their performance and durability. The shape of these parts determines that the reference input of the cutting tool depends on the rotation angle of the workpiece rather than the time process, resulting in the actual signal having periodic characteristics in terms of position rather than time. Specifically, when the workpiece rotates around the main shaft, the cutting tool needs to be precisely adjusted according to the change of the rotation angle to achieve the required cutting shape. This position-related periodic characteristic poses significant challenges to traditional time-domain repetitive control systems.

[0003] To solve the above problems, researchers have integrated some adaptive methods into time-domain repetitive control systems, such as improving performance by adjusting the sampling period or buffer length of the repetitive controller. However, these methods not only increase the computational complexity but also may cause stability problems. Therefore, when dealing with the high-precision control requirements of rotating systems, choosing to adopt a position-domain control strategy becomes a more effective approach. The position-domain control strategy focuses on position-related periodic signals. Since the period of these signals is constant with respect to position and independent of the rotation speed, the controller designed in the position domain can more effectively cope with the challenges brought by the change of rotation speed. The concept of the position domain was initially introduced to suppress angle-related disturbances in constant-speed rotating systems. Compared with the time domain, the control in the position domain can track and suppress spatial periodic disturbances more accurately, ensuring high-efficiency suppression performance for position-related periodic disturbances, and thus has received extensive attention.

[0004] It is worth noting that many existing methods still rely on state-space models to describe rotating systems, resulting in the fuzzification of the physical meaning of the system and possibly the problem of ill-conditioned matrices during model simplification, thus affecting control performance and stability. In contrast, the fully actuated system is modeled based on physical laws, which can more accurately reflect the dynamic characteristics of the real system, avoid numerical calculation problems caused by ill-conditioned matrices, and retain the physical meaning of the system. This modeling method not only improves the accuracy of the model but also simplifies the design of the control system, making it more suitable for the high-precision machining of complex non-circular contour parts. Summary of the Invention

[0005] The object of the present invention is to provide a high-precision turning method, device and medium for non-circular profile parts based on high-order full drive in the position domain. First, for the rotating system, a motor voltage excitation signal is given, the tool position output signal is collected, and the second-order state space model of the rotating system in the time domain is obtained by using the Matlab system identification toolbox; secondly, aiming at the problem that the change of the time period will significantly reduce the system control performance, the definition of the position domain and a transformation method for converting the rotating system model from the time domain to the position domain are given; furthermore, according to the obtained position domain model, it is further discretized and converted into a high-order full drive model; subsequently, a corresponding full drive control law is designed to stabilize the system; finally, a model predictive controller is designed to solve the optimal control law and inverse transform it into a full drive control law through the corresponding relational expression, so as to realize the high-precision turning of non-circular profile parts.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A high-precision turning method for non-circular profile parts in the position domain, including:

[0008] Step S1, for the rotating system, a motor voltage excitation signal is given, the tool position output signal is collected, and the second-order state space model of the rotating system in the time domain is obtained by using the system identification toolbox;

[0009] Step S2, aiming at the problem that the change of the time period will significantly reduce the control performance of the rotating system, the definition of the position domain is given, and the time domain model of the rotating system is converted into a position domain model through a transformation method;

[0010] Step S3, according to the obtained position domain model, the position domain model is discretized and converted into a high-order full drive model, and then a corresponding full drive stabilizing controller is designed to stabilize the rotating system;

[0011] Step S4, design a model predictive controller to solve the optimal control law and inverse transform it into a full drive control law through the corresponding relational expression.

[0012] Further, the second-order state space model of the rotating system obtained in step S1 is:

[0013] (1)

[0014] Where represents the state of the rotating system, represents the derivative of the state of the rotating system with respect to time, represents the tool position output signal, represents the motor voltage excitation signal, represents the state matrix of the rotating system, represents the control matrix of the rotating system, Represents the output matrix of the rotation system.

[0015] Furthermore, the step S2 includes:

[0016] Define as the rotational speed of the rotation system, , then any position in the time domain can be expressed as:

[0017] (2)

[0018] where, is the position corresponding to the moment , is the integration variable, the position domain is a set of positions defined by a series of equations (2), and the time-domain signal is represented in the position domain as :

[0019] (3)

[0020] and The relationship of is , and the inverse function of equation (2) is given by:

[0021] (4)

[0022] where, represents the rotational speed of the system in the position domain. Substituting equation (2) into equation (1), the derivative of the rotation system state can be expressed as:

[0023] (5)

[0024] where, represents the rotation system state in the position domain. Taking as the independent variable of the rotation system state, the rotation system state space model in the position domain is:

[0025] (6)

[0026] where, and are respectively the tool position output signal and the motor voltage excitation signal in the position domain.

[0027] Furthermore, the step S3 includes:

[0028] Define the constant The relationship with the current turntable rotational speed is , and at the same time considering the rotation system identification parameters and , the equations of the rotational system are written as:

[0029] (7)

[0030] where are system identification parameters. Taking the derivative of yields , where represents the second derivative of . Substituting the equation about in Equation (7) and eliminating variables gives:

[0031] (8)

[0032] Discretizing Equation (8) according to the increment of the rotation angle, the following high-order fully actuated model can be obtained:

[0033] (9)

[0034] where , respectively represent the 1-step and 2-step recursions of , , are all intermediate variables, , , ;

[0035] Based on the high-order fully actuated theory, if the coefficient matrix is invertible, the rotational system is fully actuated; using the direct parameter method to design a fully actuated stabilizing controller, the designed has the following form:

[0036] (10)

[0037] where is the parameter matrix of the designed fully actuated stabilizing controller, is an external signal;

[0038] Substituting Equation (9) into Equation (8) to convert the original rotational system into a fully actuated form:

[0039] (11).

[0040] Furthermore, the step S4 includes:

[0041] Denote as the augmented matrix composed of , , , , there is:

[0042] (12)

[0043] Among them, represents a 1-step recursion of is the identity matrix of appropriate dimension;

[0044] For the reference input position signal in the position domain derived from the rotation angle of the main shaft motor, design a model predictive controller to solve the optimal control law; set the prediction interval

[0045] (13)

[0046] where is the augmented matrix composed of represents for of step recursion, represents for of step recursion, respectively represent of 2, , , power;

[0047] Define the quadratic performance index as:

[0048] (14)

[0049] where represents the state weight matrix of the rotating system, represents the control weight matrix of the rotating system, represents the matrix transpose symbol, is the augmented matrix composed of , is the augmented matrix composed of is the reference input position signal in the position domain, and The relationship between

[0050]

[0051] where respectively represent for of Step-by-step recursion;

[0052] Solve the quadratic performance index through the Yalmip toolbox to obtain the optimal control sequence ;

[0053] Take the first element of the sequence as the system control law at the current moment, and according to Equation (10), inverse transform the external signal obtained by the MPC controller through Equation (10) into and substitute into the high-order fully actuated model in the position domain shown in Equation (9) to achieve high-precision turning of non-circular profile parts.

[0054] The present invention also provides a high-precision turning processing device for non-circular profile parts in the position domain, characterized in that it includes one or more processors for implementing a high-precision turning processing method for non-circular profile parts in the position domain as described above.

[0055] The present invention also provides a readable storage medium with a program stored thereon, which when executed by a processor, implements a high-precision turning processing method for non-circular profile parts in the position domain as described above.

[0056] Compared with the prior art, the beneficial effects of the present invention are:

[0057] 1) Aiming at the problem that the change of the time period will significantly reduce the system control performance, the present invention gives the definition of the position domain and a transformation method for converting the rotating system model from the time domain to the position domain;

[0058] 2) The present invention uses a fully actuated system model to characterize the rotating system in the position domain, which can not only maintain the physical interpretability of the model, but also avoid the ill-conditioned matrix problem that often appears in traditional methods. At the same time, it also significantly improves the efficiency and simplicity of the design process;

[0059] 3) The present invention proposes an MPC method based on a high-order fully actuated model, and converts the obtained optimal control law back to the control instruction applicable to the fully actuated system through the corresponding inverse transformation relation, and finally realizes high-precision tracking of the periodic reference input in the position domain. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flow chart of a high-precision turning processing method for non-circular profile parts in the position domain of the present invention.

[0061] Figure 2 It is a comparison curve graph of the actual cutting trajectory and the reference trajectory of the turning tool in the high-precision turning processing method for non-circular profile parts in the position domain of the present invention.

[0062] Figure 3 This is a schematic structural diagram of a high-precision turning machining device for non-circular contour parts in the position domain of the present invention. Specific embodiments

[0063] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0064] Please refer to Figure 1 and Figure 2 , a high-precision turning machining method for non-circular contour parts in the position domain, comprising the following steps:

[0065] Step S1: For the rotation system (the rotation drive system of the lathe spindle), a motor voltage excitation signal is given, the tool position output signal is collected, and a second-order state space model of the rotation system in the time domain is obtained by using the system identification toolbox. The system identification toolbox can use Matlab:

[0066] Among them, the second-order state space model of the rotation system is as follows:

[0067] (1)

[0068] Among them, represents the state of the rotation system, represents the derivative of the rotation system state with respect to time, represents the tool position output signal, represents the motor voltage excitation signal, represents the state matrix of the rotation system, represents the control matrix of the rotation system, represents the output matrix of the rotation system. In the present invention .

[0069] Step S2: To address the problem that the change in the time period will significantly reduce the control performance of the rotation system, the definition of the position domain is given, and the rotation system model is transformed from the time domain model to the position domain model through a transformation method, specifically including:

[0070] Define as the rotational speed of the rotation system, , then any position in the time domain can be expressed as:

[0071] (2)

[0072] Among them, is the moment The corresponding position is the integration variable. The position domain is a set of positions defined by a series of equations (2). In the present invention, the time-domain signal is expressed in the position domain as :

[0073] (3)

[0074] and The relational expression of is , and the inverse function of equation (2) is given by the following formula:

[0075] (4)

[0076] Wherein, represents the system rotational speed in the position domain. Substituting equation (2) into equation (1), the derivative of the rotational system state can be expressed as:

[0077] (5)

[0078] Wherein, represents the rotational system state in the position domain. Taking as the independent variable of the rotational system state, the rotational system state space model in the position domain is:

[0079] (6)

[0080] Wherein, and are respectively the tool position output signal and the motor voltage excitation signal in the position domain.

[0081] Step S3: According to the obtained position domain model, further discretize the position domain model and convert it into a high-order fully actuated model, and then design a corresponding fully actuated stabilizing controller to stabilize the rotational system, specifically including:

[0082] Define the constant and the relationship with the current turntable rotational speed is , in the present invention , and at the same time considering the rotational system identification parameters and , then the equation of the rotational system can be written as:

[0083] (7)

[0084] In the present invention, , , then equation (7) is:

[0085]

[0086] Derive with respect to , and we can obtain , where represents the second derivative of . Substitute the equation about in equation (7) and eliminate the variables to get:

[0087] (8)

[0088] Discretize equation (8) according to the increment of the rotation angle, and the following high-order fully actuated model can be obtained:

[0089] (9)

[0090] where , respectively represent the 1-step and 2-step recursions of , , are all intermediate variables, , , . Specifically, , , .

[0091] Based on the high-order fully actuated theory, if the coefficient matrix is invertible, then the rotation system is fully actuated. Design a fully actuated stabilizing controller using the direct parameter method. The designed has the following form:

[0092] (10)

[0093] where is the parameter matrix of the designed fully actuated stabilizing controller. In the present invention, , is an external signal.

[0094] Substitute equation (9) into equation (8) to convert the original rotation system into a fully actuated form:

[0095] (11).

[0096] Step S4: Design a model predictive controller to solve the optimal control law and inverse-transform it into a fully actuated control law through the corresponding relationship, specifically including:

[0097] Denote as The augmented matrix formed , , , then there is:

[0098] (12)

[0099] wherein, represents one-step recursion of is the identity matrix of appropriate dimension.

[0100] For the reference input position signal in the position domain derived from the rotation angle of the main shaft motor , design a model predictive controller to solve the optimal control law. Set the prediction interval , and the recursive expression is as follows:

[0101] (13)

[0102] where is the augmented matrix formed represents for step recursion of represents for step recursion of respectively represent the 2nd, 3rd, 4th, and 5th powers of

[0103] ,

[0104] .

[0105] where T represents the matrix transpose symbol.

[0106] Define the quadratic performance index as:

[0107] (14)

[0108] wherein, represents the state weight matrix of the rotating system, represents the control weight matrix of the rotating system, represents the matrix transpose symbol, is the augmented matrix formed , is an external signal. is the augmented matrix formed is the reference input position signal in the position domain, and are related as follows:

[0109]

[0110] wherein, respectively represent the for step-by-step recurrence.

[0111] The quadratic performance index J is solved through the Yalmip toolbox to obtain the optimal control sequence .

[0112] Take the first element of the sequence as the system control law at the current moment, and according to Equation (10), the external signal obtained by the MPC controller is inversely transformed through Equation (10) into , and is substituted into the high-order fully actuated model in the position domain shown in Equation (9) to achieve high-precision turning of non-circular profile parts. The final machining trajectory of the non-circular profile parts is as Figure 2 shown.

[0113] See Figure 3 . An apparatus for high-precision turning of non-circular profile parts in the position domain provided by an embodiment of the present invention includes one or more processors for implementing a method for high-precision turning of non-circular profile parts in the position domain in the above embodiment.

[0114] An embodiment of an apparatus for high-precision turning of non-circular profile parts in the position domain according to the present invention can be applied to any device with data processing capabilities. The any device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented by software, or by hardware or a combination of software and hardware. Taking software implementation as an example, as a logically meaningful device, it is formed by the processor of any device with data processing capabilities where it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for operation. From the hardware level, as Figure 3 shown, is a hardware structure diagram of any device with data processing capabilities where an apparatus for high-precision turning of non-circular profile parts in the position domain according to the present invention is located. In addition to Figure 3 the shown processor, memory, network interface, and non-volatile memory, any device with data processing capabilities where the device in the embodiment is located usually further includes other hardware according to the actual functions of the any device with data processing capabilities, which will not be elaborated here.

[0115] For the implementation processes of the functions and roles of the units in the above device, please refer to the implementation processes of the corresponding steps in the above method for details, which will not be elaborated here.

[0116] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered to be within the scope described in this specification.

[0117] The embodiment of the present invention also provides a readable storage medium, on which a program is stored. When the program is executed by a processor, it implements a high-precision turning machining method for non-circular contour part position domain in the above embodiment.

[0118] The readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or memory. The readable storage medium may also be an external storage device, such as a plug-in hard disk, a Smart Media Card (SMC), an SD card, a Flash Card, etc. equipped on the device. Further, the readable storage medium may also include both an internal storage unit of any device with data processing capabilities and an external storage device. The readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and can also be used to temporarily store the data that has been output or will be output.

[0119] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A high-precision turning method for non-circular contour parts in the position domain, characterized in that, Including: Step S1: For the rotary system, a motor voltage excitation signal is given, the tool position output signal is collected, and the second-order state space model of the rotary system in the time domain is obtained by using the system identification toolbox. The second-order state space model of the rotary system is: (1) Among them, represents the rotational system state, denotes the derivative of the rotational system state with respect to time, represents the tool position output signal, represents the motor voltage excitation signal, denotes the state matrix of the rotational system, denotes the control matrix of the rotational system, denotes the output matrix of the rotational system; Step S2: Aiming at the problem that the change of the time period will significantly reduce the control performance of the rotary system, the definition of the position domain is given, and the time domain model of the rotary system is transformed into the position domain model through a transformation method, including: Definition is the rotational speed of the rotation system, , then any position in the time domain can be expressed as: (2) wherein, is the position corresponding to the time instant , is the integration variable, the position domain is a set of positions defined by a series of formulas (2), and the time-domain signal is represented in the position domain as : (3) and The relational expression is , and the inverse function of Equation (2) is given by the following formula: (4) Among them, represents the system rotational speed under the position domain. Substituting Equation (2) into Equation (1), the derivative of the rotational system state can be expressed as: (5) Among them, represents the rotation system state in the position domain. Taking as the independent variable of the rotation system state, the rotation system state space model in the position domain is: (6) Among them, and are the tool position output signal and the motor voltage excitation signal under the position domain respectively; Step S3: According to the obtained position domain model, the position domain model is discretized and converted into a high-order fully actuated model, and then a corresponding fully actuated stabilizing controller is designed to stabilize the rotary system; Step S4: Design a model predictive controller to solve the optimal control law and inverse transform it into the fully actuated control law through the corresponding relationship.

2. A high-precision turning method for non-circular contour parts in the position domain according to claim 1, characterized in that The said step S3 includes: Define constants With the current turntable rotation speed The relationship is , while considering the rotational system identification parameters and , then the equation of the rotational system is written as: (7) Among them, is the system identification parameter. Taking the derivative of , we can obtain , where represents the second derivative of . Substituting the equation about in Equation (7) for elimination, we get: (8) Discretize Equation (8) according to the increment of the rotation angle to obtain the following high-order fully actuated model: (9) Among them, , respectively represent the 1st and 2nd step recursions of , , are all intermediate variables, , , ; Based on the high-order full-drive theory, if the coefficient matrix is invertible, then the rotational system is full-driven; the full-driven stabilizing controller is designed by the direct parameter method, and the design has the following form: (10) in is the parameter matrix of the designed all-wheel drive stabilization controller, is an external signal; Substitute equation (9) into equation (8) to convert the original rotary system into a fully actuated form: (11)。 3. A high-precision turning method for non-circular contour parts in a position domain according to claim 2, characterized in that, The said step S4 includes: Denote as the augmented matrix formed by , , , then we have: (12) Among them, denotes a 1-step recurrence of and is the identity matrix of appropriate dimension; For the reference input position signal in the position domain derived from the rotation angle of the spindle motor , design a model predictive controller to solve the optimal control law; set the prediction interval , and the recurrence expression is as follows: (13) wherein is the augmented matrix formed, denotes for of step recurrence, denotes for of step recurrence, respectively denote to the powers of 2, , , powers; Define the quadratic form performance index as follows: (14) Among them, represents the state weight matrix of the rotation system, represents the control weight matrix of the rotation system, represents the matrix transpose symbol, is the augmented matrix formed by, , is the augmented matrix formed by, is the reference input position signal in the position domain, and are related as follows: Among them, respectively represent for of stepwise recurrence; Solve the quadratic performance index through the Yalmip toolbox to obtain the optimal control sequence ; Take the first element of the sequence as the system control law at the current moment, and according to Equation (10), reverse-transform the external signal obtained by the MPC controller back to through Equation (10), and substitute into the high-order fully actuated model in the position domain shown in Equation (9) to achieve high-precision turning of non-circular profile parts.

4. A high-precision turning machining device for non-circular contour parts in the position domain, characterized in that, Comprising one or more processors for implementing a high-precision turning machining method for non-circular profile parts in the position domain according to any one of claims 1-3.

5. A readable storage medium, characterized in that, Stored thereon is a program which, when executed by the processor, implements a high-precision turning machining method for non-circular profile parts in the position domain according to any one of claims 1-3.

Images