Evaluation method and system for interpolation instruction of numerical control system

Abstract

The invention discloses a numerical control system interpolation instruction evaluation method and system, and relates to the technical field of numerical control machine tools, and the method comprises the following steps: carrying out the discrete Fourier transform of an interpolation instruction sequence, and obtaining the frequencies and amplitudes of a plurality of point sequences in the interpolation instruction sequence; obtaining an interpolation instruction frequency domain index based on the amplitudes and frequencies of the plurality of point sequences; decomposing the interpolation instruction sequence into a stable part and a time-varying part, and performing Hilbert-Huang transform on the time-varying part to obtain instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part; obtaining an interpolation instruction time-frequency domain index based on the instantaneous frequency, the instantaneous amplitude and the instantaneous phase information of the time-varying part; and evaluating the interpolation instruction through the interpolation instruction frequency domain index and the interpolation instruction time-frequency domain index. By analyzing the frequency domain index and the time-frequency domain index of the interpolation instruction, the corresponding relation between the instruction and the servo system and the machine tool structure can be researched, and the final machining precision of the numerical control machine tool is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical control machine tools, and in particular to a method and system for evaluating interpolation instructions of a numerical control system. Background Art

[0002] The interpolation instructions generated by CNC system interpolation (the process of discretizing and reconstructing the target motion trajectory through mathematical methods) serve as input to the servo feed system of a CNC machine tool. The frequency components they contain directly affect the dynamic accuracy of the CNC machine tool. Due to differences in interpolation algorithms, different CNC systems still generate certain differences in the interpolation instructions when interpolating the same part machining program. Therefore, it is necessary to analyze and evaluate the interpolation instructions generated by CNC system interpolation to reflect the CNC system's ability to achieve the dynamic accuracy of the machine tool. Generally speaking, the larger the frequency components contained in the interpolation instructions, the more difficult it is for the servo system to fully respond, ultimately affecting the dynamic accuracy of the machine tool and the processing accuracy of the part. In addition, the interpolation instructions should contain fewer high-frequency components to avoid inertial forces causing vibration in the mechanical structure.

[0003] Currently, the time domain analysis method alone can intuitively observe the change of the interpolation instruction amplitude over time, but cannot obtain the frequency component in the interpolation instruction; and the frequency domain analysis method alone can only obtain the frequency component in the entire interpolation instruction, but cannot determine the part path position corresponding to the frequency component.

[0004] To address these issues, a Chinese patent application (CN201810967645.0) evaluates CNC system interpolation instructions from a time-domain / time-frequency domain perspective. This primarily includes interpolation instruction displacement, velocity, acceleration, and jerk indicators. By directly observing the temporal variations of these indicators or analyzing their time-frequency plots, the authors assess the impact of their dynamic characteristics on machine tool accuracy. A Chinese patent application (CN202010445410.2) evaluates CNC system interpolation instructions from a frequency-domain perspective. This approach defines a frequency spectrum curve for the interpolation instructions, solves the frequency spectrum curve and magnification function for each cross-section, and defines an interpolation instruction evaluation method based on the attenuation magnification of the servo feed system. However, this method only analyzes CNC system interpolation instructions and proposes preliminary evaluation criteria. This lacks a quantitative and in-depth analysis of the instructions, making it impossible to study the correspondence between the instructions and the servo system and machine tool structure, making it difficult to guarantee the ultimate machining accuracy of the machine tool. Summary of the Invention

[0005] Based on the defects of the above-mentioned existing technologies, the present invention provides a method and system for evaluating interpolation instructions of a CNC system, which solves the problems that the existing methods lack quantitative and in-depth analysis of instructions, cannot study the correspondence between instructions and servo systems and machine tool structures, and are difficult to ensure the final processing accuracy of machine tools.

[0006] The present invention adopts the following technical solutions:

[0007] In a first aspect, the present invention provides a method for evaluating an interpolation instruction of a numerical control system, comprising the following steps:

[0008] Run the G code corresponding to the part's motion trajectory in the CNC system, and collect the interpolation instruction sequence to be evaluated during the operation;

[0009] Performing discrete Fourier transform on the interpolation instruction sequence to obtain the frequencies and amplitudes of multiple point sequences in the interpolation instruction sequence; obtaining the total amplitude of the interpolation instruction sequence based on the amplitudes of the multiple point sequences, and obtaining the frequency domain index of the interpolation instruction based on the frequencies and total amplitudes of the multiple point sequences;

[0010] The interpolation instruction sequence is decomposed into a stable part and a time-varying part. The time-varying part is subjected to Hilbert-Huang transform to obtain the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part. The time-frequency domain indicators of the interpolation instruction are obtained based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part.

[0011] The interpolation instructions are evaluated by the interpolation instruction frequency domain index and the interpolation instruction time-frequency domain index.

[0012] Preferably, performing discrete Fourier transform on the interpolation instruction sequence to obtain frequency and amplitude information of multiple point sequences in the interpolation instruction sequence specifically includes the following steps:

[0013] Performing discrete Fourier transform on the collected interpolation instruction sequence to obtain a first transformation formula;

[0014] Based on Euler's formula, the first transformation formula is rewritten to obtain the second transformation formula;

[0015] Based on the real and imaginary parts in the second transformation formula, the frequency and amplitude information of multiple point sequences are obtained, as shown below:

[0016]

[0017] Where, f k is the frequency corresponding to the k-th point sequence, f s is the sampling frequency of the interpolation instruction sequence s, A Kis the amplitude of the k-th point sequence, Real(k) is the real part in the second transformation formula, Imag(k) is the imaginary part in the second transformation formula, and N is the length of the interpolation instruction sequence of the CNC system.

[0018] Preferably, the step of obtaining the interpolation instruction frequency domain index according to the frequency and total amplitude of the plurality of point sequences comprises the following steps:

[0019] The interpolation instruction frequency domain index is the overall frequency domain bandwidth index. The point sequence where the overall frequency domain bandwidth is located is defined as bw. According to the frequency and total amplitude of multiple point sequences, the following inequality is obtained:

[0020]

[0021] Where P1 is the actual amplitude corresponding to the first point sequence after Fourier transform, P2 is the actual amplitude corresponding to the second point sequence, and P bw-1 is the actual amplitude corresponding to the bw-1th point sequence, P bw is the actual amplitude corresponding to the bw-th point sequence, BW is the frequency domain bandwidth coefficient, and P is the total amplitude;

[0022] According to the above inequality, the frequency corresponding to the overall frequency domain bandwidth is:

[0023] f bw =f s (bw-1) / N;

[0024] Where, f bw It is the overall frequency domain bandwidth value of the interpolation instruction, which is used to reflect the frequency distribution of the interpolation instruction.

[0025] Preferably, the interpolation instruction sequence is decomposed into a stable part and a time-varying part, and the stable part and the time-varying part are specifically as follows:

[0026]

[0027] Where F(t) is the stable part, a0 is the constant term, and a m and b m is the expansion coefficient of the mth harmonic, ω0 is the fundamental frequency of the stable part, R(t) is the time-varying part, and x(t) is the interpolation instruction in the machine tool coordinate system.

[0028] Preferably, performing Hilbert-Huang transform on the time-varying part to obtain the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part comprises the following steps:

[0029] The time-varying part is preprocessed by empirical mode decomposition, and the preprocessing results are as follows:

[0030]

[0031] Where y i (t) is the component obtained by decomposition, r(t) is the remainder, t is the time, and n is the number of times the instruction experience pattern is decomposed;

[0032] For the component y i The analytical signal of (t) is defined as:

[0033]

[0034] Where, is the component y i (t) is the analytical signal, H[*] is the Hilbert operator, and τ is the integration constant;

[0035] pass Get the component y i The analytical function of (t):

[0036]

[0037] Where z i (t) is the analytical function of the i-th component, A i (t) is the instantaneous amplitude function, φ i (t) is the instantaneous phase function;

[0038] Frequency is the rate of change of phase with time, so the instantaneous frequency ω of the i-th component is i (t) is:

[0039]

[0040] Preferably, the step of obtaining the time-frequency domain index of the interpolation instruction based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part comprises the following steps:

[0041] The interpolation instruction time-frequency domain indicators include a box plot, a scatter plot, a first curve graph and a second curve graph;

[0042] Obtaining a box plot based on the instantaneous frequency of the time-varying part, wherein the box plot is used to reflect the overall distribution of the instantaneous frequency of the interpolation instruction;

[0043] A scatter plot is obtained based on the instantaneous frequency and instantaneous phase information of the time-varying part, wherein the scatter plot is used to reflect the frequency distribution of the interpolation instruction at each time;

[0044] Acquire a first curve graph based on the maximum instantaneous frequency and instantaneous phase information of the time-varying portion, wherein the first curve graph is used to reflect the change of the maximum instantaneous frequency of the interpolation instruction;

[0045] The comprehensive parameters describing the potential excitation are determined based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part, as shown below:

[0046]

[0047] Where j is the number of interpolation cycles, m is the frequency count after Hilbert-Huang transform, M is the total number of frequencies after Hilbert-Huang transform, f(t,m) is the frequency after Hilbert-Huang transform, a(t,f) is the amplitude at the corresponding time and frequency after Hilbert-Huang transform; ω(f) is the frequency weight;

[0048] A second curve graph is obtained based on the potential excitation comprehensive parameters and time or G code, and the second curve graph is used to reflect the potential excitation situation at the instant of the interpolation instruction or the G code line number.

[0049] Preferably, before running the G code corresponding to the part motion trajectory in the numerical control system, it is necessary to set the maximum velocity of the trajectory in the G code, and set the maximum acceleration and maximum jerk of the trajectory in the numerical control system.

[0050] In a second aspect, the present invention provides an evaluation device for an interpolation instruction of a numerical control system, comprising:

[0051] The acquisition module is used to run the G code corresponding to the part's motion trajectory in the CNC system and collect the interpolation instruction sequence to be evaluated during the operation;

[0052] The frequency domain processing module is used to perform discrete Fourier transform on the interpolation instruction sequence to obtain the frequency and amplitude of multiple point sequences in the interpolation instruction sequence; obtain the total amplitude of the interpolation instruction sequence based on the amplitude of the multiple point sequences, and obtain the interpolation instruction frequency domain index according to the frequency and total amplitude of the multiple point sequences;

[0053] The time-frequency domain processing module is used to decompose the interpolation instruction sequence into a stable part and a time-varying part, perform Hilbert-Huang transform on the time-varying part to obtain the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part; and obtain the time-frequency domain indicators of the interpolation instruction based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part;

[0054] The evaluation module is used to evaluate the interpolation instruction through the interpolation instruction frequency domain index and the interpolation instruction time-frequency domain index.

[0055] Compared with the prior art, the at least one technical solution adopted by the present invention can achieve the following beneficial effects:

[0056] The present invention first collects the interpolation instruction sequence to be evaluated, performs discrete Fourier transform on the interpolation instruction sequence, and obtains the frequency and amplitude of multiple point sequences in the interpolation instruction sequence; performs frequency domain decomposition and analysis on the instruction, and determines the total amplitude of the interpolation instruction sequence based on the analysis results, obtains the interpolation instruction frequency domain index based on the frequency and total amplitude of the multiple point sequences, and the index is used to reflect the frequency distribution of the interpolation instruction. By comparing the frequency distribution of the interpolation instruction with the servo bandwidth, the response relationship between the interpolation instruction and the servo system can be obtained.

[0057] At the same time, the interpolation instruction sequence is decomposed into a stable part and a time-varying part whose frequency components vary with time. The time-varying part is subjected to Hilbert-Huang transform to obtain the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part; based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part, the interpolation instruction time-frequency domain index is obtained; this index is used to reflect the overall distribution of the instantaneous frequency of the interpolation instruction, the frequency distribution at each time, the maximum instantaneous frequency change and the potential excitation at the instantaneous moment. These conditions are actually correlated with the machine tool structure or servo system. Therefore, by analyzing the interpolation instruction frequency domain index and time-frequency domain index of the present invention, the correspondence between the instruction and the servo system and the machine tool structure can be studied, thereby improving the final processing accuracy of the CNC machine tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0059] Figure 1 A flowchart of a method for evaluating an interpolation instruction of a numerical control system according to the present invention;

[0060] Figure 2 This is a time domain analysis diagram of an interpolation instruction according to an embodiment of the present invention;

[0061] in, Figure 2 (a): displacement map of the instruction, Figure 2 (b): Speed diagram of the instruction, Figure 2 (c): acceleration diagram of the instruction;

[0062] Figure 3 This is a frequency domain analysis diagram of interpolation instructions according to an embodiment of the present invention;

[0063] in, Figure 3 (a): Overall spectrum of instructions, Figure 3(b): Locally enlarged spectrum of the instruction;

[0064] Figure 4 This is a frequency distribution diagram of the stable part of the interpolation instruction according to an embodiment of the present invention;

[0065] Figure 5 This is a schematic diagram of the time-varying portion of the interpolation instruction according to an embodiment of the present invention;

[0066] Figure 6 This is a frequency distribution diagram of the time-varying portion of the interpolation instruction according to an embodiment of the present invention;

[0067] Figure 7 The time-varying partial Hilbert spectrum of the interpolation instruction according to an embodiment of the present invention;

[0068] Figure 8 is a box diagram of the potential excitation instantaneous frequency of the interpolation instruction according to an embodiment of the present invention;

[0069] Figure 9 This is a scatter plot of the potential excitation instantaneous frequency of the interpolation instruction according to an embodiment of the present invention;

[0070] Figure 10 This is a graph showing the maximum instantaneous frequency of potential excitation of an interpolation instruction according to an embodiment of the present invention;

[0071] Figure 11 A dot-line diagram of potential excitation positions of interpolation instructions according to an embodiment of the present invention. DETAILED DESCRIPTION

[0072] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0073] Based on the technical problems existing in the prior art, the present invention provides a method for evaluating the interpolation instructions of a numerical control system, referring to Figure 1 , specifically including the following steps:

[0074] S1: Design a motion trajectory and write G code.

[0075] Design a CNC machining motion trajectory for a part, use CAM software to generate the interpolation point sequence corresponding to the G code, and then write the G code according to the requirements of different CNC systems.

[0076] S2: Set the maximum velocity of the trajectory to F, the maximum acceleration to a, and the maximum jerk to j; complete the operation within time t and collect the interpolation instruction sequence.

[0077] Set the maximum velocity of the trajectory to F in the G code, and set the maximum acceleration and maximum jerk of the trajectory to a and j in the CNC system, respectively. Enter the G code into the corresponding CNC system, execute it within time t, and use the CNC system's built-in data acquisition function to collect the interpolation instructions generated according to the CNC system's interpolation cycle. This acquisition process obtains information such as the instruction sequence and G code line number.

[0078] S3: Perform frequency domain analysis on the interpolation instruction sequence and propose frequency domain indicators for interpolation instructions.

[0079] S31: Perform discrete Fourier transform on the instruction to determine its frequency and corresponding amplitude and phase information.

[0080] Assume that the G code of a part is interpolated by the CNC system and the interpolation instruction in the machine tool coordinate system is recorded as x(t). The first transformation formula can be obtained by performing discrete Fourier transform on the collected discrete non-periodic instruction sequence x(iΔT):

[0081]

[0082] Where X(k) represents the data after discrete Fourier transform, x(iΔT) is the position sequence generated by the CNC system, i represents the sampling point sequence in the time domain, ΔT is the interpolation period of the CNC system, k represents the kth point sequence in the frequency domain, N is the interpolation instruction length of the CNC system, j is the imaginary unit, e is the Euler number, and π is the circumference of pi.

[0083] Since the position sequences interpolated by the actual CNC system are all real signals, that is, the imaginary part of x(iΔT) is zero. Therefore, according to the Euler formula e jx =cosx+jsinx, the above formula can be transformed into the second transformation formula:

[0084]

[0085] After performing discrete Fourier transform on the instruction sequence, the real and imaginary parts of the instruction sequence X(k) are:

[0086]

[0087] According to the above formula, after discrete Fourier transform, the frequency, amplitude and phase corresponding to the k-th point of the instruction are:

[0088]

[0089] Where, f k is the frequency corresponding to the k-th point sequence, A K and are the amplitude and phase at the corresponding frequency, f s is the sampling frequency of instruction sequence s.

[0090] S32: Defines the overall frequency domain bandwidth indicator of the instruction.

[0091] Due to the symmetry of the discrete Fourier transform results, the actual amplitude corresponding to the kth point in equation (4) is:

[0092]

[0093] The total magnitude of the instruction is:

[0094] P=∑P k k=1,2,3,…(6);

[0095] Define the location of the overall frequency domain bandwidth of the instruction as bw, that is:

[0096]

[0097] Where P1 is the actual amplitude corresponding to the first point after Fourier analysis, P2 is the actual amplitude corresponding to the second point, and P bw-1 is the actual amplitude corresponding to the bw-1th point, P bw is the actual amplitude corresponding to the bw-th point, BW is the instruction frequency domain bandwidth coefficient related to the geometric parameters of the analyzed instruction, and bw is the point sequence corresponding to the instruction frequency domain bandwidth frequency.

[0098] According to the above formula, the frequency corresponding to the overall frequency domain bandwidth of the instruction is:

[0099] f bw =f s (bw-1) / N (8);

[0100] The overall frequency bandwidth of a command is determined by the frequency position corresponding to the command's frequency amplitude. This metric reflects the frequency distribution of the command. The servo bandwidth of a servo system reflects the range within which it can respond to a command. If the servo bandwidth of a servo system is greater than the overall frequency bandwidth of the command, the command can be effectively responded to.

[0101] S4: Analyze the time-frequency domain performance of the interpolation instruction sequence and propose time-frequency domain indicators for interpolation instructions.

[0102] Specifically, the instruction sequence is decomposed into a stable part and a time-varying part, and the time-varying part is analyzed in the time-frequency domain to solve its instantaneous frequency and the corresponding instantaneous amplitude and instantaneous phase information, and the time-frequency domain indicators of the interpolation instruction are proposed.

[0103] S41: Decompose the instruction into a stable part and a time-varying part: The n-th order Fourier series fitting and interpolation instruction time-varying part of the instruction x(t) can be expressed as:

[0104]

[0105] In the formula, a0 is a constant term, a m and b m is the expansion coefficient of the mth harmonic, and ω0 is the fundamental frequency of the stable portion. The command x(t) is decomposed into two parts. F(t) is the sum of multiple sine and cosine signals and a constant term (DC component). This term's frequency component does not change over time and is used to represent the stable portion of the command. R(t) is the residual term, which has insufficient fitting accuracy and has a drastically varying frequency component. It is used to represent the time-varying portion of the command.

[0106] S42: Use the Hilbert-Huang Transform to further decompose the time-varying portion of the instruction: Since the Hilbert-Huang Transform has very high requirements for the input instruction, the remainder of most instructions cannot be directly decomposed. Therefore, before solving the instantaneous frequency of the time-varying part R(t), it is necessary to pre-process R(t) using empirical mode decomposition (EMD). EMD continuously subtracts the mean of the upper and lower envelopes of the signal to be processed from the signal to be processed, and finally decomposes the signal to be processed into multiple basic mode components and a remainder, which is:

[0107]

[0108] For the component y i Hilbert-Huang transform of (t) The analytical signal is defined as:

[0109]

[0110] Construct the component y i The analytical function of (t) is defined as:

[0111]

[0112] Where y i (t) is the decomposed component, r(t) is the remainder, is the component y i The analytical signal of (t), z i (t) is the analytical function of the i-th component; A i (t) is the instantaneous amplitude function; φ i (t) is the instantaneous phase function.

[0113] Frequency is the rate of change of phase with time, so the instantaneous frequency of the i-th component is:

[0114]

[0115] S43: Defines the potential excitation frequency size index of the instruction.

[0116] Combining equations (13) and (14) we can further obtain the Hilbert spectrum H(w,t):

[0117]

[0118] Where, ω i (t) is the instantaneous frequency function, H(w,t) represents the Hilbert spectrum, Re represents the real part, and the Hilbert spectrum describes the relationship between instantaneous frequency, instantaneous amplitude and instantaneous phase. The time (instantaneous phase) and instantaneous frequency information in the Hilbert spectrum can be used to establish a potential excitation frequency index.

[0119] S431: Box plot showing potential excitation frequency range:

[0120] The instantaneous frequency information of the time-varying portion of the instruction is plotted as a box plot. The box plot contains the maximum instantaneous frequency, minimum instantaneous frequency, median instantaneous frequency, upper and lower quartiles of the instantaneous frequency, and other information. This metric reflects the overall distribution of the instantaneous frequency. The larger the maximum instantaneous frequency, minimum instantaneous frequency, median instantaneous frequency, and upper and lower quartiles of the instantaneous frequency in the box plot, the more significant the high-frequency transient component in the interpolation instruction, placing higher demands on the high-frequency response capability of the CNC system. During the forward design of the machine tool structure, it is important to ensure that the first-order natural frequency of the structure is greater than the maximum instantaneous frequency in the box plot to avoid resonance.

[0121] S432: Scatter plot showing potential stimulus frequency distribution:

[0122] The instantaneous frequency and time information of the time-varying portion of the command are plotted as a scatter plot. The scatter plot contains the time and instantaneous frequency corresponding to each point. This metric reflects the frequency distribution at each time point. Areas where high-frequency points are clustered in the scatter plot indicate moments of dramatic command dynamics, potentially causing tracking lag, overshoot, or even hardware damage. When designing the servo model for a servo system, it is important to pay attention to the frequency response during periods of high-frequency point clustering.

[0123] S433: The curve graph shows the maximum frequency information of potential excitation:

[0124] The maximum instantaneous frequency and time information of the time-varying portion of the instruction are plotted as a graph, which includes the maximum instantaneous frequency value at each moment. This metric can reflect the variation of the maximum instantaneous frequency. The peak duration and amplitude in the graph represent the transient impact strength of the interpolation instruction. If the peak exceeds the system closed-loop bandwidth or the physical limits of the actuator, it will lead to a decrease in phase margin and the excitation of high-frequency resonance. This metric needs to be analyzed when designing servo models and tracing the vibration marks on the part surface.

[0125] S44: Defines the potential excitation frequency position index of the instruction.

[0126] The potential excitation frequency position index can be established by using the time (instantaneous phase), instantaneous frequency, and instantaneous amplitude information in the Hilbert spectrum in Equation (15). The determination of the excitation position must consider both the frequency value and the corresponding amplitude. Therefore, it is necessary to determine a comprehensive parameter that describes the potential excitation, as follows:

[0127]

[0128] Where j is the number of interpolation cycles, the time after Hilbert-Huang transform t = iΔT; m is the frequency count after Hilbert-Huang transform, f(t,m) is the frequency after Hilbert-Huang transform, and when the interpolation time is constant, f(m) = mf H , f H is the frequency resolution of the Hilbert-Huang transform; a(t,f) is the amplitude at the corresponding time and frequency after the Hilbert-Huang transform; ω(f) is the frequency weight, which is defined as follows:

[0129]

[0130] Where, f is the frequency after Hilbert-Huang transformation, f bw is the overall frequency domain bandwidth of the interpolation instruction of the CNC system; ω(f) indicates that when the frequency of the Hilbert-Huang transform is less than the instruction bandwidth, its value is 0, otherwise it is 1.

[0131] Plotting the potential excitation comprehensive parameter against time or G-code creates a curve, corresponding to the potential excitation at that instant or G-code line. This metric reflects the potential excitation of the instruction, and the peak value of the potential excitation comprehensive parameter reflects the actual surface quality of the machined part. More peaks in the potential excitation comprehensive parameter indicate more potential excitation in that instruction and more surface chatter marks on the part. Higher peaks indicate greater energy in the excitation and more pronounced surface chatter marks.

[0132] Example

[0133] Taking the analysis of the interpolation round-trip trajectory instructions of the GNC60 CNC system as an example, a CNC system interpolation and speed planning performance analysis and evaluation method includes the following steps:

[0134] 1) Specifically: design a round-trip motion trajectory, use CAM software to generate the corresponding G code, and write the G code according to the requirements of the GNC60 numerical control system as shown in Table 1.

[0135] Table 1 G code of this embodiment

[0136] N1 G40 G17 G90 G21 N2 G227 N3 G204 N4 G216 N5 CG52 N6 G239 T0.02A0.01 N7 G203 N8 G54 N9 G1 X0 Y0 Z0 A0 C0 F20000 N10G237 A1 D65 C2 N11G01 X200 F20000 N12G1 X0 N13G1 X100 F10000 N14G1 X0 N15G1 X100 F10000 N16G1 X0 N17G238 N18M30

[0137] 2) Specifically: Set the maximum speed of the round-trip trajectory to 20000mm / min in the G code, and set the maximum acceleration and maximum jerk of the round-trip trajectory to 0.9mm / s in the GNC60 numerical control system. -2 and 250 mm / s -3 ; Input the round-trip trajectory G code into the GNC60 numerical control system, the running time is 4.58s, use the data acquisition function of the GNC60 numerical control system, set the interpolation cycle to 2ms, and collect the generated interpolation instructions. By collecting the instruction sequence and G code line number, the displacement, velocity and acceleration curves of the round-trip trajectory are drawn as shown in the figure. Figure 2 shown.

[0138] 3) Specifically, the frequency domain analysis of round-trip instructions is performed, and the frequency domain index of interpolation instructions is proposed.

[0139] 3.1) Assume that the G code of the round-trip trajectory is interpolated by the GNC60 numerical control system to obtain the interpolation instruction in the machine tool coordinate system, which is recorded as x(t). The discrete Fourier transform of the collected discrete non-periodic instruction sequence x(iΔT) can be obtained by discrete Fourier transforming the data X(k).

[0140]

[0141] After the round-trip instruction is decomposed by discrete Fourier, the frequency, amplitude and phase corresponding to each point of the instruction X(k) can be solved. The spectrum diagram is drawn according to the frequency, amplitude and phase information solved by the round-trip trajectory, as shown in the following figure: Figure 3 As shown, it can be seen that the instructions of the round-trip trajectory are mainly concentrated in the low-frequency part.

[0142] 3.2) Define the overall frequency domain bandwidth indicator for round-trip instructions:

[0143] The total amplitude of the round-trip trajectory interpolation instruction is:

[0144] P=∑P k k=1,2,3,…(19);

[0145] Define the overall frequency domain bandwidth of the instruction as bw, and take BW as 0.9999, that is,

[0146]

[0147] According to the above formula, the frequency corresponding to the overall frequency domain bandwidth of the round-trip trajectory interpolation instruction is:

[0148] f bw =f s (bw-1) / N=19.4Hz (21);

[0149] The overall frequency domain bandwidth of a command is determined by the frequency position corresponding to the command frequency domain amplitude. This indicator can reflect the frequency distribution of the command. If the servo system's servo bandwidth is greater than the overall frequency domain bandwidth of the command, the command can be well responded to.

[0150] 4) Specifically, the round-trip trajectory instruction is decomposed into a stable part and a time-varying part, and the time-varying part is analyzed in the time-frequency domain to solve its instantaneous frequency and the corresponding instantaneous amplitude and instantaneous phase information, and the time-frequency domain indicators of the interpolation instruction are proposed.

[0151] 4.1) Decompose the round-trip trajectory command into a stable part and a time-varying part, where F(t) is the sum of multiple sine and cosine signals and a constant term (DC component), as follows: Figure 4 As shown in the figure, the frequency component of this item does not change with time and is used to characterize the stable part of the instruction; R(t) is the residual item with insufficient fitting accuracy, and the frequency component in this item changes dramatically, such as Figure 5 The term shown represents the time-varying portion of the instruction.

[0152] 4.2) Use Hilbert-Huang Transform to further decompose the time-varying part of the round-trip trajectory interpolation instruction: Since Hilbert-Huang Transform has very high requirements for input instructions, the remainder of most instructions cannot be directly decomposed. Therefore, before solving the instantaneous frequency of the time-varying part R(t), it is necessary to pre-process R(t) using EMD. EMD continuously subtracts the mean of the upper and lower envelopes of the signal to be processed from the signal to be processed, and finally decomposes the signal to be processed into multiple basic mode components and a remainder. According to the Hilbert-Huang Transform and the solution method of instantaneous frequency, the instantaneous frequency of each basic mode component is as follows: Figure 6 shown.

[0153] 4.3) Define the potential excitation frequency size index of round-trip instructions:

[0154] The Hilbert spectrum H(w,t) can be further obtained by using analytical functions and instantaneous frequency, as follows: Figure 7 The Hilbert spectrum shown describes the relationship between instantaneous frequency, instantaneous amplitude and instantaneous phase; the time (instantaneous phase) and instantaneous frequency information in the Hilbert spectrum can be used to establish a potential excitation frequency size index.

[0155] 4.3.1) Box plots represent the potential excitation frequency range:

[0156] The instantaneous frequency information of the time-varying part of the round-trip trajectory interpolation instruction is plotted as a box plot, which includes the maximum instantaneous frequency, the minimum instantaneous frequency, the median of the instantaneous frequency, the upper and lower quartiles of the instantaneous frequency, etc. Figure 8 As shown in Figure 2, this indicator can reflect the overall distribution of instantaneous frequency.

[0157] 4.3.2) Scatter plot showing the frequency distribution of potential excitations:

[0158] The instantaneous frequency and time information of the time-varying part of the round-trip trajectory interpolation instruction are plotted as a scatter plot, which contains the time and instantaneous frequency corresponding to each point. Figure 9 As shown in Figure 2, this indicator can reflect the frequency distribution at each time.

[0159] 4.3.3) The curve graph shows the maximum frequency information of potential excitation:

[0160] The maximum instantaneous frequency and time information of the time-varying part of the round-trip trajectory interpolation instruction are plotted as a curve graph, which contains the maximum instantaneous frequency value at each moment. Figure 10 As shown in Figure 2, this indicator can reflect the maximum instantaneous frequency change.

[0161] 4.4) Define the potential excitation frequency position index of the round trip instruction:

[0162] The potential excitation frequency position index can be established by using the time (instantaneous phase), instantaneous frequency and instantaneous amplitude information in the Hilbert spectrum. The determination of the excitation position must take into account both the frequency value and the corresponding amplitude.

[0163] The potential excitation comprehensive parameters and time or G code are plotted as a dot-line graph, corresponding to the potential excitation situation at the instant or G code line number. Figure 11 As shown in Figure 3, this indicator can reflect the potential incentive of the round-trip instruction. The more peak points of the potential incentive comprehensive parameter, the more potential incentives there are for the instruction; the higher the peak value, the greater the energy of the incentive.

[0164] The present invention provides a method for analyzing and evaluating the interpolation and speed planning performance of a numerical control system. The method compiles corresponding G codes according to motion trajectories, collects interpolation instructions, analyzes and decomposes the instructions using frequency domain and time-frequency domain analysis methods, and solves their frequency, amplitude, and phase, thereby obtaining evaluation indicators of the instructions, thereby realizing analysis and evaluation of the interpolation and speed planning performance of the numerical control system.

[0165] The present invention can provide CNC machine tool R&D manufacturers with optimization directions and goals for servo feed system optimization, interpolation algorithm optimization, speed planning algorithm optimization, etc. when designing and developing servo feed systems and optimizing interpolation and speed planning algorithms of CNC systems.

[0166] Based on the same concept, the present invention also provides an evaluation system for interpolation instructions of a numerical control system, comprising an acquisition module, a frequency domain processing module, a time-frequency domain processing module and an evaluation module.

[0167] The acquisition module is used to run the G code corresponding to the part's motion trajectory in the CNC system and collect the interpolation instruction sequence to be evaluated during the operation;

[0168] The frequency domain processing module is used to perform discrete Fourier transform on the interpolation instruction sequence to obtain the frequency and amplitude of multiple point sequences in the interpolation instruction sequence; obtain the total amplitude of the interpolation instruction sequence based on the amplitude of the multiple point sequences, and obtain the interpolation instruction frequency domain index according to the frequency and total amplitude of the multiple point sequences;

[0169] The time-frequency domain processing module is used to decompose the interpolation instruction sequence into a stable part and a time-varying part, perform Hilbert-Huang transform on the time-varying part to obtain the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part; and obtain the time-frequency domain indicators of the interpolation instruction based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part;

[0170] The evaluation module is used to evaluate the interpolation instruction through the interpolation instruction frequency domain index and the interpolation instruction time-frequency domain index.

[0171] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0172] Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if such modifications and variations fall within the scope of the claims and their equivalents, the present invention is intended to include such modifications and variations.

Claims

1. A method for evaluating interpolation instructions of a numerical control system, characterized in that: The following steps are involved: Run the G code corresponding to the part's motion trajectory in the CNC system, and collect the interpolation instruction sequence to be evaluated during the operation; Performing discrete Fourier transform on the interpolation instruction sequence to obtain the frequencies and amplitudes of multiple point sequences in the interpolation instruction sequence; obtaining the total amplitude of the interpolation instruction sequence based on the amplitudes of the multiple point sequences, and obtaining the frequency domain index of the interpolation instruction based on the frequencies and total amplitudes of the multiple point sequences; The interpolation instruction sequence is decomposed into a stable part and a time-varying part. The time-varying part is subjected to Hilbert-Huang transform to obtain the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part. The time-frequency domain indicators of the interpolation instruction are obtained based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part. The interpolation instructions are evaluated by the interpolation instruction frequency domain index and the interpolation instruction time-frequency domain index.

2. The method for evaluating an interpolation instruction of a numerical control system according to claim 1, wherein: The discrete Fourier transform is performed on the interpolation instruction sequence to obtain frequency and amplitude information of multiple point sequences in the interpolation instruction sequence, which specifically includes the following steps: Performing discrete Fourier transform on the collected interpolation instruction sequence to obtain a first transformation formula; Based on Euler's formula, the first transformation formula is rewritten to obtain the second transformation formula; Based on the real and imaginary parts in the second transformation formula, the frequency and amplitude information of multiple point sequences are obtained, as shown below: Where, f k is the frequency corresponding to the k-th point sequence, f s is the sampling frequency of the interpolation instruction sequence s, A K is the amplitude of the k-th point sequence, Real(k) is the real part in the second transformation formula, Imag(k) is the imaginary part in the second transformation formula, and N is the length of the interpolation instruction sequence of the CNC system.

3. The method for evaluating an interpolation instruction of a numerical control system according to claim 2, wherein: The method of obtaining the interpolation instruction frequency domain index according to the frequency and total amplitude of the plurality of point sequences comprises the following steps: The interpolation instruction frequency domain index is the overall frequency domain bandwidth index. The point sequence where the overall frequency domain bandwidth is located is defined as bw. According to the frequency and total amplitude of multiple point sequences, the following inequality is obtained: Where P1 is the actual amplitude corresponding to the first point sequence after Fourier transform, P2 is the actual amplitude corresponding to the second point sequence, and P bw-1 is the actual amplitude corresponding to the bw-1th point sequence, P bw is the actual amplitude corresponding to the bw-th point sequence, BW is the frequency domain bandwidth coefficient, and P is the total amplitude; According to the above inequality, the frequency corresponding to the overall frequency domain bandwidth is: f bw =f s (bw-1) / N; Where, f bw is the overall frequency domain bandwidth frequency of the interpolation instruction N, and the overall frequency domain bandwidth is used to reflect the frequency distribution of the interpolation instruction.

4. The method for evaluating an interpolation instruction of a numerical control system according to claim 1, wherein: The interpolation instruction sequence is decomposed into a stable part and a time-varying part, and the stable part and the time-varying part are specifically as follows: Where F(t) is the stable part, a0 is the constant term, and a m and b m is the expansion coefficient of the mth harmonic, ω0 is the fundamental frequency of the stable part, R(t) is the time-varying part, and x(t) is the interpolation instruction in the machine tool coordinate system.

5. The method for evaluating an interpolation instruction of a numerical control system according to claim 4, wherein: The Hilbert-Huang transform is performed on the time-varying part to obtain the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part, comprising the following steps: The time-varying part is preprocessed by empirical mode decomposition, and the preprocessing results are as follows: Where y i (t) is the component obtained by decomposition, r(t) is the remainder, t is the time, and n is the number of times the instruction experience pattern is decomposed; For the component y i The analytical signal of (t) is defined as: Where, is the component y i (t) is the analytical signal, H[*] is the Hilbert operator, and τ is the integration constant; pass Get the component y i The analytical function of (t): Where z i (t) is the analytical function of the i-th component, A i (t) is the instantaneous amplitude function, φ i (t) is the instantaneous phase function; Frequency is the rate of change of phase with time, so the instantaneous frequency ω of the i-th component is i (t) is:

6. A method for evaluating an interpolation instruction of a numerical control system according to claim 5, characterized in that: The method of obtaining the time-frequency domain index of the interpolation instruction based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part includes the following steps: The interpolation instruction time-frequency domain indicators include a box plot, a scatter plot, a first curve graph and a second curve graph; Obtaining a box plot based on the instantaneous frequency of the time-varying part, wherein the box plot is used to reflect the overall distribution of the instantaneous frequency of the interpolation instruction; A scatter plot is obtained based on the instantaneous frequency and instantaneous phase information of the time-varying part, wherein the scatter plot is used to reflect the frequency distribution of the interpolation instruction at each time; Acquire a first curve graph based on the maximum instantaneous frequency and instantaneous phase information of the time-varying portion, wherein the first curve graph is used to reflect the change of the maximum instantaneous frequency of the interpolation instruction; Based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part, the comprehensive parameters describing the potential excitation are determined as follows Where j is the number of interpolation cycles, m is the frequency count after Hilbert-Huang transform, M is the total number of frequencies after Hilbert-Huang transform, f(t,m) is the frequency after Hilbert-Huang transform, a(t,f) is the amplitude at the corresponding time and frequency after Hilbert-Huang transform; ω(f) is the frequency weight; A second curve graph is obtained based on the potential excitation comprehensive parameters and time or G code, and the second curve graph is used to reflect the potential excitation situation at the instant of the interpolation instruction or the G code line number.

7. The method for evaluating an interpolation instruction of a numerical control system according to claim 1, wherein: Before running the G code corresponding to the part motion trajectory in the CNC system, it is necessary to set the maximum velocity of the trajectory in the G code and set the maximum acceleration and maximum jerk of the trajectory in the CNC system.

8. An evaluation device for interpolation instructions of a numerical control system, characterized in that: include: The acquisition module is used to run the G code corresponding to the part's motion trajectory in the CNC system and collect the interpolation instruction sequence to be evaluated during the operation; The frequency domain processing module is used to perform discrete Fourier transform on the interpolation instruction sequence to obtain the frequency and amplitude of multiple point sequences in the interpolation instruction sequence; obtain the total amplitude of the interpolation instruction sequence based on the amplitude of the multiple point sequences, and obtain the interpolation instruction frequency domain index according to the frequency and total amplitude of the multiple point sequences; The time-frequency domain processing module is used to decompose the interpolation instruction sequence into a stable part and a time-varying part, perform Hilbert-Huang transform on the time-varying part to obtain the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part; and obtain the time-frequency domain indicators of the interpolation instruction based on the instantaneous frequency, instantaneous amplitude and instantaneous phase information of the time-varying part; The evaluation module is used to evaluate the interpolation instruction through the interpolation instruction frequency domain index and the interpolation instruction time-frequency domain index.

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