A CNC machine tool machining accuracy analysis method based on discrete sampling and response transients

Abstract

This invention discloses a method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response. It establishes a time decay model for the CNC machine tool, collects input and output data, and uses a hybrid particle swarm optimization (PSO) and gradient descent algorithm to identify model parameters. Machining errors are discretely sampled using a sampling period T. The error sample values ​​at each sampling time are used as input and convolved with the impulse response model. The convolution output is divided into steady-state and transient outputs, and a recursive equation incorporating historical transient summations is established. With the minimum sum of squared machining errors as the optimization objective, a PSO algorithm is used to search for the sampling period and tool feed gain that minimize the objective, and the CNC machine tool control parameters are set accordingly. This invention establishes the response model, the transient relationship between control input and output without changing the hardware. By optimizing control parameters, surface ripple is suppressed, and machining errors are reduced. The model is identified solely based on input and output data.

Description

Technical Field

[0001] This invention relates to a method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and response transients, belonging to the field of CNC machine tool machining control. Background Technology

[0002] Numerical control machine tools (NC machine tools) effectively solve the problems of machining complex, precise, small-batch, and multi-variety parts. They are flexible and highly efficient automated machine tools. NC machine tools offer high precision and flexible machining capabilities, enabling them to complete complex surface machining tasks. They are widely used in high-end manufacturing fields such as aerospace, mold manufacturing, and medical devices.

[0003] The machining accuracy of machine tools directly reflects the level of the manufacturing industry. Improving the machining accuracy of CNC machine tools is a crucial research direction in the field. During CNC machining, the machine tool uses a computer to discretely sample machining parameters in time and controls the tool feed and cutting parameters based on parameter errors. Improving control accuracy based on the sampling results is key to enhancing the machining accuracy of CNC machine tools.

[0004] Computer systems are digital systems and can only process discrete digital signals. Real-time sampling in CNC machine tools can only be discrete, periodic digital signal sampling. Within a sampling period, the tool control signal can only be calculated based on the most recent sampling result to obtain the control output, control the tool feed, and thus control the cutting parameters.

[0005] No machine is perfect, and machining workpieces is no exception. Tool feed inevitably generates cutting force, and under this force, the workpiece will inevitably produce a transient response. This response changes over time, ultimately affecting the depth of cut: with the same tool feed, different depths of cut affect the surface finish of the workpiece. In CNC machine tool periodic sampling control, one transient process follows another, resulting in overlapping transient processes and causing ripples on the workpiece surface.

[0006] Although a great deal of research has been conducted on how to improve the machining accuracy of CNC machine tools, there is a lack of research on CNC machine tools that focuses on discrete sampling from computers and transient processes of cutting response. Summary of the Invention

[0007] This invention provides a method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and response transients to address the problems existing in the prior art.

[0008] The technical solutions adopted in this invention are as follows:

[0009] A method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response includes the following steps:

[0010] (1) Collect input and output data in the feed direction of the CNC machine tool, and use the particle swarm and gradient hybrid algorithm to identify the impulse response model of the machining system that decays over time;

[0011] (2) Discretely sample the machining error with sampling period T, generate tool feed signal based on sampling results, convolve the tool feed signal as input with the impulse response model, establish a recursive equation for the change of workpiece machining error with time, and include the time interval corresponding to the current sampling period and the transient superposition of sampling signals from all previous sampling periods in the recursive equation.

[0012] (3) Taking the minimization of the sum of squared processing errors as the optimization objective, the particle swarm optimization algorithm is used to search for the sampling period that minimizes the objective. With tool feed gain and based on the determined Set the control parameters for CNC machine tools.

[0013] Furthermore, the impulse response model is as follows:

[0014] ,

[0015] in, , Parameters to be identified Represents the coefficient. This represents the power of the impulse response.

[0016] Furthermore, the recursive equation is:

[0017] ,

[0018] in, For the workpiece at time Total machining error; This is the tool feed gain; For the first Error sampling value at the start of each sampling period; For a fixed sampling period; Indicates the first The start time point of each sampling period; and Let u(t−nT)−u(t−(n+1)T) be the unit step function, used to indicate the time interval t∈(nT,(n+1)T). Indicates from the first The sampling period to the 1st sampling period Between each sampling period, due to the input in The transient output generated at a given time point , For responding to transient states, use the abbreviation "Transient".

[0019] Furthermore, the termination condition of the particle swarm algorithm is that the change in the global optimum value is less than a preset threshold for two consecutive generations or the number of iterations reaches a set upper limit.

[0020] Furthermore, the input and output data are discrete sampling sequences in the tool feed direction, and the sampling length covers the historical period when the impulse response decays to a preset amplitude ratio.

[0021] Furthermore, the particle swarm optimization and gradient hybrid algorithm first uses a global particle swarm optimization search, and then uses a gradient method to refine the identification parameters locally.

[0022] Furthermore, the initial range of the sampling period T is determined jointly based on the highest sampling frequency and the lowest machining efficiency requirements of the CNC machine tool servo system.

[0023] Furthermore, the tool feed gain The initial value range is constrained by the maximum feed acceleration allowed by the machine tool servo system and the cutting force limit.

[0024] Furthermore, the sum of squared processing errors only selects error sampling values ​​from a finite historical period before the current moment for calculation, and the length of the historical period is determined by the time constant of the impulse response decaying to below the threshold.

[0025] The present invention has the following beneficial effects:

[0026] (1) Without changing the machine tool hardware, adjusting only the sampling period and the tool feed gain can reduce the surface ripple amplitude and reduce the sum of squared machining errors under the same cutting conditions.

[0027] (2) A simple power-law response model is used instead of the traditional differential equation to avoid complex mechanism modeling. The model parameters are obtained only by identifying the input and output data. The implementation examples have verified that the model is consistent with the measured error trend and the model is effective.

[0028] (3) The particle swarm-gradient hybrid algorithm is used to complete the joint tuning of model parameters and control parameters in one go. The reduction of the square integral of the error is used as the criterion, and it can be reproduced without additional hardware. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the CNC machine tool machining process;

[0030] Figure 2 As described in the embodiments of the present invention , Simulation diagram of machining error;

[0031] Figure 3 As described in the embodiments of the present invention , Simulation diagram of machining error. Detailed Implementation

[0032] The invention will now be further described with reference to the accompanying drawings.

[0033] This invention addresses the problem of improving machining accuracy in CNC machine tools. Starting from discrete sampling and transient response characteristics, it establishes the response characteristics of the machining process. Using discrete sampled signals as input, and combining these with the response characteristics, it analyzes the transient process of cutting, and then analyzes the factors affecting the machining accuracy of CNC machine tools based on this transient process, providing a basis for optimizing machining accuracy. To solve the machining accuracy problem caused by the superposition of discrete sampling and transient response during CNC machine tool machining, this embodiment combines the response characteristics and discrete sampling rules of the machining system, achieving accuracy improvement through system modeling, transient analysis, and parameter optimization. A schematic diagram of the CNC machine tool machining process is shown below. Figure 1 As shown, the present invention specifically includes the following steps:

[0034] (1) First, the machining process of a CNC machine tool is considered as a whole system, which includes machining parameter sampling, retainer, tool feed control and workpiece response, etc. The focus is on studying the input-output characteristics of this system. In traditional studies, machining parameter errors are usually established. With tool feed rate The differential equation for displacement is solved based on the parameter error, i.e.:

[0035] (1.1),

[0036] in, It is about The nonlinear function, and according to , , These represent the ideal impulse function and the convolution operation, respectively.

[0037] The above differential model can be regarded as an ideal impulse response model, but in reality it is almost impossible to establish a mathematical model as shown in formula (1.1) based on the complex mechanism of CNC machine tools.

[0038] Therefore, this invention establishes a system response model through input-output relationships, identifies system parameters to construct an impulse response model, and obtains the impulse response model of the CNC machine tool along the tool feed direction as follows:

[0039] (1.2),

[0040] in, Represents the coefficient. The impulse response is expressed as a power, and both are parameters to be identified. Since any physically realizable system is a bounded-input bounded-output system, its impulse response is always a function that decays with time. Therefore, this model can accurately describe the system response characteristics.

[0041] It should be noted that any physically realizable system is always a bounded input and bounded output system, and CNC machine tools are no exception. According to the condition that the impulse response of a bounded system is absolutely integrable, the impulse response is always a function that decays with time and can always be represented by the model in formula (2.1).

[0042] This invention utilizes the Legendre transform to convert the convolutional model into an algebraic model and constructs a cost function. Experiments were conducted to collect input and output data from a CNC machine tool. Due to the... (2.2) It is not sensitive to gradient information. To balance convergence speed, it combines particle swarm optimization and gradient search algorithms to identify unknown model parameters. , The input-output impact response model of the CNC machine tool was obtained. .

[0043] (2) Combining periodic discrete sampling, analyze the transient process of processing and the factors affecting processing accuracy, specifically including the following steps:

[0044] (2.1) Set the sampling time interval of the CNC machine tool to be... The initial sampling time is set to 0, and the discrete sampling times are successively set to 0. , , , ,in Indicates the first At the next sampling time, the corresponding tool feed rate is denoted as... , , , , .

[0045] (2.2) Based on the sampling hold principle, the tool feed can be expressed as a continuous-time function as:

[0046] (2.1),

[0047] in It is a unit step function.

[0048] (2.3) Based on the response characteristics, establish the parameter error equations for the workpiece after machining:

[0049] (2.2),

[0050] in, This represents the tool feed gain obtained based on the measurement error.

[0051] (2.4) Replace the tool feed rate with the machining error sample value in the input to obtain the error equation corresponding to the error input: (2.3).

[0052] (2.5) Study the workpiece machining error output in time segments:

[0053] (1) When At that time, only the input at the initial sampling moment has an impact, and at this time:

[0054] (2.4);

[0055] (2) When When considering the transient state of the initial sampled input and the influence of the current sampled input, the following should be taken into account:

[0056] (2.5)

[0057] It should be noted that, although the input signal The length is However, based on the properties of convolution, The length is infinite, meaning the input is cut off, but the output is not. There is also a transient state, and this transient state will continue indefinitely. Therefore, the processing error can be obtained:

[0058] (2.6);

[0059] For simplicity, let's remember... , indicating that because Input within a time period The transient output generated within a time period.

[0060] The same applies below: Indicates due to Input within the time period The transient output generated within a time period.

[0061] (3) When At this time, the transient effects of the input from the previous two sampling cycles and the current sampling input need to be taken into account.

[0062] (2.7)

[0063] same resemblance,

[0064] (2.8).

[0065] (4) When At that time, the machining error equation is:

[0066] (2.9)

[0067] Ultimately, we can obtain:

[0068] (3.0).

[0069] in, For the workpiece at time Total machining error; This refers to the tool feed gain, i.e., the tool feed gain. ; For the first Error sampling value at the start of each sampling period; For a fixed sampling period; Indicates the first The start time point of each sampling period; and It is a unit step function. Indicates from the first The sampling period to the 1st sampling period Between each sampling period, due to the input in The transient output generated at a given time point , For responding to transient states, use the abbreviation "Transient".

[0070] In formula (3.0), the first part represents the output generated by the current sampled input control signal, and the second part represents the output transient generated by the historical sampled input control signals, which does not disappear and will forever affect subsequent processes. Similarly, the current output is not only affected by the current sampled input, but also by all times before the current time.

[0071] Equation (3.0) shows that the roughness of the machined workpiece surface on a CNC machine tool is due to the discrete periodic sampling and transient processes during machining. The superposition of periodic sampling and transient processes generates transient oscillations, creating ripples on the machined workpiece surface and thus affecting machining accuracy. The sampling period is directly related to the workpiece ripple period, and the tool feed gain is directly related to the transient oscillation amplitude, which in turn affects the workpiece surface ripple amplitude, dimensional accuracy, and surface finish.

[0072] Although all historical samples will affect the current transient oscillation and the machining accuracy, formula (3.0) also shows that the transient process decays over time, and the further back in time the sampling is from the current time, the smaller the impact on machining accuracy. Historical samples that do not significantly affect accuracy analysis can be ignored. Therefore, analysis can be performed by combining historical samples within a certain historical length range at the current sampling time. The specific historical length depends on the impulse response decay characteristics of the CNC machine tool machining system and the allowable range of analysis error.

[0073] The above segmented analysis clearly shows that the ripple on the machined surface of a CNC machine tool is caused by the combined effect of discrete periodic sampling and transient processes during machining. The sampling period is directly related to the ripple period and the tool feed gain. It affects the transient oscillation amplitude, which in turn affects the surface finish and dimensional accuracy; at the same time, the transient decays over time, and the impact of long-term sampling can be ignored, only the sampling input of a finite historical period before the current moment needs to be considered.

[0074] Finally, with the goal of minimizing the sum of squared processing errors, the cost function is constructed as follows:

[0075] (3.1),

[0076] By optimizing control parameters (i.e., selecting appropriate tool feed gain and sampling period), an optimal control strategy is formulated for different workpieces to improve machining accuracy. Since formula (3.1) is not sensitive to gradient information of tool feed gain and sampling period, a particle swarm optimization (PSO) algorithm is used for parameter search. First, initial settings are performed to determine the particle swarm size, initial position (i.e., the initial values ​​of period and gain in the control parameters), and initial velocity. The initial range of the sampling period is determined by the highest sampling frequency and the minimum machining efficiency requirement of the CNC machine tool servo system, and the initial range of the tool feed gain is constrained by the maximum allowable feed acceleration and cutting force limit of the machine tool servo system. Then, the cost function of each particle is calculated to obtain the current optimal value of each particle. The velocity and position of each particle are then updated, and the cost function is recalculated after the update. This process is repeated until the termination condition is met, i.e., the change of the global optimal value for two consecutive generations is less than the preset threshold or the number of iterations reaches the set upper limit. At this time, the loop is terminated, and the optimal control parameters are obtained. The optimal control parameters are set into the control system of the CNC machine tool, and the machining effect is verified by simulation or physical experiment. The machining quality of the workpiece is compared to verify the effectiveness of this method.

[0077] like Figure 2 and Figure 3 In the specific simulation verification, a discrete sampling period is selected. The impulse response model adopts the formula shown in equation (2.2). Choose different forms Value and tool feed gain Perform simulation tests, for example when , as well as , Simulation results of the corresponding machining errors were obtained. By comparing the simulation data under different parameter combinations, the influence of the parameters, sampling period and tool feed gain of the model shown in formula (2.2) on the machining accuracy was further verified. It was also proved that the control parameters obtained by the particle swarm algorithm optimization can significantly reduce machining errors and improve machining quality.

[0078] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response, characterized in that: Includes the following steps: (1) Collect input and output data in the feed direction of the CNC machine tool, and use the particle swarm and gradient hybrid algorithm to identify the impulse response model of the machining system that decays over time; (2) Discretely sample the machining error with sampling period T, generate tool feed signal based on sampling results, convolve the tool feed signal as input with the impulse response model, establish a recursive equation for the change of workpiece machining error with time, and include the time interval corresponding to the current sampling period and the transient superposition of sampling signals from all previous sampling periods in the recursive equation. (3) Taking the minimization of the sum of squared processing errors as the optimization objective, the particle swarm optimization algorithm is used to search for the sampling period that minimizes the objective. With tool feed gain and based on the determined Set the control parameters for CNC machine tools.

2. The method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response as described in claim 1, characterized in that: The impulse response model is as follows: ， in, , Parameters to be identified Represents the coefficient. This represents the power of the impulse response.

3. The method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response as described in claim 2, characterized in that: The recursive equation is: ， in, For the workpiece at time Total machining error; This is the tool feed gain; For the first Error sampling value at the start of each sampling period; For a fixed sampling period; Indicates the first The start time point of each sampling period; and Let u(t-nT)-u(t-(n+1)T) be the unit step function, used to indicate the time interval t∈(nT,(n+1)T). Indicates from the first The sampling period to the 1st sampling period Between each sampling period, due to the input in The transient output generated at a given time point , For responding to transient states, use the abbreviation "Transient".

4. The method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response as described in claim 1, characterized in that: The termination condition for the particle swarm optimization algorithm is that the change in the global optimum value is less than a preset threshold for two consecutive generations or the number of iterations reaches a set upper limit.

5. The method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response as described in claim 1, characterized in that: The input and output data are discrete sampling sequences in the tool feed direction, and the sampling length covers the historical period when the impulse response decays to a preset amplitude ratio.

6. The method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response as described in claim 1, characterized in that: The particle swarm optimization and gradient hybrid algorithm first uses particle swarm optimization for global search, and then uses gradient optimization to refine the identification parameters locally.

7. The method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response as described in claim 1, characterized in that: The initial range of the sampling period T is determined by the highest sampling frequency and the lowest machining efficiency requirement of the CNC machine tool servo system.

8. The method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response as described in claim 1, characterized in that: The tool feed gain The initial value range is constrained by the maximum feed acceleration allowed by the machine tool servo system and the cutting force limit.

9. The method for analyzing the machining accuracy of CNC machine tools based on discrete sampling and transient response as described in claim 1, characterized in that: The sum of squared processing errors is calculated using only error sample values ​​from a finite historical period before the current moment. The length of the historical period is determined by the time constant during which the impulse response decays to below the threshold.

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