A thrust prediction method and system of a direct drive feeding system considering a machining process

Abstract

The application provides a machining process considering direct drive feeding system thrust prediction method and system, including the following steps: step 1, acquiring the frequency characteristics of the cutting force in three directions of the direct drive feeding system in the machining process; step 2, calculating the mechanical vibration response of the direct drive feeding system under the disturbance of the cutting force obtained in step 1; step 3, according to the mechanical vibration response obtained in step 2, calculating the servo drive current and motor air gap magnetic field considering the mechanical vibration response; step 4, according to the obtained servo drive current and motor air gap magnetic field considering the mechanical vibration response, calculating the linear motor thrust considering the machining process; step 5, according to the obtained linear motor thrust, predicting the thrust of the direct drive feeding system; the application can comprehensively calculate and analyze the thrust spectrum characteristics of the linear motor considering the machining process of the parts, and has important significance for revealing the causes of the thrust fluctuation problems in the actual engineering application of the linear motor, and further structure optimization and control compensation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of motor driving and control, and particularly relates to a thrust prediction method and system of a direct drive feeding system considering a machining process. BACKGROUND

[0002] The direct drive feeding system driven by a permanent magnet synchronous linear motor cancels all intermediate mechanical transmission links, can realize "zero transmission" of the feeding motion, has the advantages of simple structure, large stiffness, high feeding speed and good motion performance, and has a good application prospect in the fields of robots, rail transportation and high-speed machine tools. However, without the buffering of the transmission link, the thrust harmonics generated by the nonlinearities of the driving circuit and the motor structure directly act on the mechanical system, causing significant displacement fluctuation and affecting the motion performance of the feeding system. Therefore, domestic and foreign scholars have carried out a large amount of research work on the thrust fluctuation problem of the linear motor, and have proposed various structure optimization and control compensation methods, which have important significance for improving the thrust fluctuation and motion accuracy of the direct drive feeding system.

[0003] However, in the application of high-speed machine tools, the performance advantages of the direct drive feeding system have not been fully utilized. In the related research work of thrust analysis and calculation, the permanent magnet synchronous linear motor itself is mainly considered, and the dynamic characteristics of the driving system and the application scenarios are not paid enough attention to. Especially in the machining process of complex parts of high-speed machine tools, the influence law of the machining process on the thrust characteristics of the direct drive feeding system has not been fully revealed, and there is a large error between the motor thrust prediction and the actual situation, which leads to a large number of harmonic components in the motor thrust in the actual application, affecting the motion performance of the feeding system and the final part machining accuracy, and restricting the application and popularization of the direct drive feeding system. SUMMARY

[0004] The purpose of the present application is to provide a thrust prediction method and system of a direct drive feeding system considering a machining process, which solves the problem of incomplete characterization of the thrust characteristics of the linear motor in the prior art, realizes accurate prediction of the motor thrust in the machining process, and provides a theoretical basis for error tracing of the feeding system and further structure optimization and control compensation.

[0005] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0006] The thrust prediction method of the direct drive feeding system considering the machining process provided by the present application comprises the following steps:

[0007] Step 1, acquiring the frequency characteristics of the cutting force in three directions of the direct drive feeding system in the machining process;

[0008] Step 2, calculate the mechanical vibration response of the direct drive feeding system under the disturbance of the cutting force obtained in step 1;

[0009] Step 3, according to the mechanical vibration response obtained in step 2, calculate the servo driving current and motor air gap magnetic field considering the mechanical vibration response;

[0010] Step 4, according to the obtained servo driving current and motor air gap magnetic field, calculate the linear motor thrust considering the machining process;

[0011] Step 5, according to the obtained linear motor thrust, predict the thrust of the direct drive feeding system.

[0012] Preferably, in step 1, the specific expression of the frequency characteristics of the direct drive feeding system in the machining process obtained is:

[0013]

[0014] Wherein, F cxj ,ω cxj , are the amplitude, frequency and phase of the jth order cutting force component along the x-axis direction; F cyj ,ω cyj , are the amplitude, frequency and phase of the jth order cutting force component along the y-axis direction; F czj ,ω czj , are the amplitude, frequency and phase of the jth order cutting force component along the z-axis direction.

[0015] Preferably, in step 2, the mechanical vibration response of the direct drive feeding system under the disturbance of the cutting force obtained in step 1 is calculated by:

[0016]

[0017] Wherein, X is the vibration output vector of the mechanical system; x c ,y c ,z c ,θ cx ,θ cy ,θ cz are the linear vibrations of the mechanical system along the x, y and z axes and the torsional vibrations around the x, y and z axes under the action of the cutting force; x ci ,ω xci , are the amplitude, frequency and phase of the i th order linear vibration along the x-axis; y ci ,ω yci , are the amplitude, frequency and phase of the i th order linear vibration along the y-axis; zci zci are the amplitude, frequency and phase of the i-th order linear vibration along the z-axis, respectively; xci θxci are the amplitude, frequency and phase of the i-th order torsional vibration around the x-axis, respectively; yci θyci are the amplitude, frequency and phase of the i-th order torsional vibration around the y-axis, respectively; zci θzci are the amplitude, frequency and phase of the i-th order torsional vibration around the z-axis, respectively.

[0018] Preferably, in step 3, the servo drive current and the motor air-gap magnetic field considering the mechanical vibration response are calculated according to the mechanical vibration response obtained in step 2, and the specific method is as follows:

[0019]

[0020]

[0021] wherein i a (t), i b (t), i c (t) are the output currents of the drive circuits a, b, c three-phase, respectively; t is time; I am , I bm , I cm are the amplitudes of the m-th order current harmonics of a, b, c three-phase, respectively; f0 is the current frequency; I ri , f ri , γ ri are the amplitudes, frequency and phase of the i-th order current input harmonics caused by the mechanical vibration, respectively; B a (x), B b (x), B c (x) are the a, b, c components of the permanent magnet air-gap magnetic field distribution considering the mechanical vibration, respectively; x is the permanent magnet stator coordinate system coordinate; λ r (x, t) and λ p (x, t) are the equivalent relative permeance functions of the mechanical roll and pitch vibrations, respectively; B ma (x), B mb (x), B mc (x) are the a, b, c components of the permanent magnet air-gap magnetic field distribution.

[0022] Preferably, in step 4, the linear motor thrust considering the machining process is calculated by the following formula:

[0023] ​​​​​​​​

[0024] Among them, F mc (t) represents the motor thrust considering the machining process; v is the feed rate; L a ,L b ,L c These are the self-inductances of the three-phase coils of the motor; M ab M ac M bc These represent the mutual inductance of the three-phase coils of the motor; N is the number of coil turns; l is the coil width; and τ is the motor pole pitch.

[0025] Preferably, in step 5, the thrust of the direct-drive feed system is predicted based on the obtained linear motor thrust. Specifically, the method is as follows:

[0026] The obtained motor thrust is subjected to spectral analysis to predict the thrust of the direct drive feed system considering the machining process. The resulting thrust of the direct drive feed system considering the machining process is shown in the following formula:

[0027] F mc (t)=F0(t)+F r (t)+F ce (t)+F cag (t)+F cee (t)+F cother (t)

[0028] Among them, F mc F(t) represents the motor thrust considering the machining process; F0(t) represents the nominal motor thrust; F r (t) represents the nominal thrust harmonics of the motor; F ce (t) represents the adjusting thrust generated by the cutting force during the machining process; F cag (t) represents the coupled thrust generated during the cutting process via the motor air gap; F cee (t) represents the coupled thrust generated during the cutting process via closed-loop feedback; F cother (t) represents the new impetus generated by other factors.

[0029] A thrust prediction system for a direct-drive feed system that takes into account the machining process includes:

[0030] The frequency characteristic acquisition unit is used to acquire the frequency characteristics of the cutting force in three directions during the machining process of the direct drive feed system;

[0031] The mechanical vibration response calculation unit is used to calculate the mechanical vibration response of the direct drive feed system under the disturbance of the obtained cutting force;

[0032] The analysis model building unit is used to calculate the servo drive current and motor air gap magnetic field considering the mechanical vibration response based on the obtained mechanical vibration response.

[0033] The thrust calculation unit is used to calculate the linear motor thrust considering the machining process based on the servo drive current and the motor air gap magnetic field that take into account the mechanical vibration response.

[0034] The prediction unit is used to predict the thrust of the direct drive feed system based on the obtained linear motor thrust.

[0035] Compared with the prior art, the present invention has the following beneficial technical effects:

[0036] The thrust prediction method for direct-drive feed systems that considers the machining process proposed in this invention, based on the traditional calculation and analysis of motor thrust characteristics, further analyzes the influence of cutting force on the complex electromechanical coupling between the servo drive system and the mechanical system during machining, and improves the characterization and calculation method of linear motor output characteristics. This method can comprehensively calculate and analyze the thrust spectrum characteristics of linear motors considering the machining process of parts, which is of great significance for revealing the causes of thrust fluctuation problems in the actual engineering applications of linear motors, as well as for further structural optimization and control compensation. Attached Figure Description

[0037] Figure 1 This is the process of calculating the thrust of a linear motor considering the machining process;

[0038] Figure 2 It is a direct drive feed system under the influence of cutting force disturbance;

[0039] Figure 3 This is a comparison of the thrust of a linear motor considering the machining process versus not considering the machining process. Detailed Implementation

[0040] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0041] like Figure 1 As shown, the present invention provides a thrust prediction method for a direct-drive feed system that takes into account the machining process, comprising the following steps:

[0042] Step 1: Obtain the frequency characteristics of the cutting force in the three directions during machining using the direct drive feed system through experimental testing or theoretical calculations.

[0043]

[0044] Among them, F cxj ,ω cxj , These represent the amplitude, frequency, and phase of the j-th order cutting force component along the x-axis; F cyj ,ω cyj , These represent the amplitude, frequency, and phase of the j-th order cutting force component along the y-axis; F czj ,ω czj , These represent the amplitude, frequency, and phase of the j-th order cutting force component along the z-axis.

[0045] Step 2: Establish the mechanical dynamics model of the direct-drive feed system, namely:

[0046]

[0047] Where X is the vibration output vector of the mechanical system; M, C, and K are the inertia matrix, damping matrix, and stiffness matrix of the direct-drive mechanical system, respectively; F l H is the vector of external forces acting on the mechanical system. F This is the force transmission matrix; and Let X be the first and second derivatives of X, respectively.

[0048] By combining the mechanical dynamics model of the direct-drive feed system with the cutting force obtained in step one, the vibration response of the mechanical system during the machining process is calculated:

[0049]

[0050] Where X is the vibration output vector of the mechanical system; x c ,y c ,z c ,θ cx ,θ cy ,θ cz These represent the linear vibrations of the mechanical system along the x, y, and z axes and the torsional vibrations about the x, y, and z axes, respectively, under the action of cutting force; x ci ,ω xci , Let represent the amplitude, frequency, and phase of the i-th order linear vibration along the x-axis; y ci ,ω yci , Let z represent the amplitude, frequency, and phase of the i-th order linear vibration along the y-axis; ci ,ω zci , Let θ represent the amplitude, frequency, and phase of the i-th order linear vibration along the z-axis; xci ,ω θxci , Let θ represent the amplitude, frequency, and phase of the i-th order torsional vibration about the x-axis; yci ,ω θyci , Let θ represent the amplitude, frequency, and phase of the i-th order torsional vibration about the y-axis; zci ,ω θzci , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the z-axis.

[0051] Step 3: Consider the vibration response of the mechanical system during the processing obtained in Step 2, such as... Figure 2 As shown, the servo drive current and the motor air gap magnetic field considering mechanical vibration response are calculated:

[0052]

[0053]

[0054] Among them, i a (t),i b (t),i c (t) represents the output current of the three phases a, b, and c of the drive circuit, respectively; t is time; I am ,I bm ,I cm Let fm be the amplitudes of the m-th order current harmonics of phases a, b, and c, respectively; f0 be the current frequency; I ... ri ,f ri ,γ ri Let B represent the amplitude, frequency, and phase of the i-th order current input harmonic caused by mechanical vibration; a (x),B b (x),B c (x) represents the a, b, and c components of the air gap magnetic field distribution of the permanent magnet considering mechanical vibration; x is the coordinate of the permanent magnet stator coordinate system; λ r (x,t) and λ p (x,t) are the equivalent relative magnetic permeability functions for mechanical roll and pitch vibrations, respectively; B ma (x),B mb (x),B mc (x) represents the a, b, and c components of the air gap magnetic field distribution of the permanent magnet, respectively. ω is the angular frequency of the motor.

[0055] Step 4: Based on the servo drive current considering the influence of mechanical vibration response and the motor air gap magnetic field, calculate the linear motor thrust considering the machining process:

[0056]

[0057] Among them, F mc (t) represents the motor thrust considering the machining process; v is the feed rate; L a ,L b ,L c These are the self-inductances of the three-phase coils of the motor; M ab M ac M bcThese represent the mutual inductance of the three-phase coils of the motor; N is the number of coil turns; l is the coil width; and τ is the motor pole pitch.

[0058] Step 5: Perform spectrum analysis on the motor thrust obtained in Step 4 to analyze the main sources of thrust harmonics in the direct drive feed system during the machining process, and guide further structural optimization and control compensation.

[0059] The obtained linear motor thrust is shown in the following formula:

[0060] F mc (t)=F0(t)+F r (t)+F ce (t)+F cag (t)+F cee (t)+F cother (t)

[0061] Among them, F mc F(t) represents the motor thrust considering the machining process; F0(t) represents the nominal motor thrust; F r (t) represents the nominal thrust harmonics of the motor; F ce (t) represents the adjusting thrust generated by the cutting force during the machining process; F cag (t) represents the coupled thrust generated during the cutting process via the motor air gap; F cee (t) represents the coupled thrust generated during the cutting process via closed-loop feedback; F cother (t) represents the new impetus generated by other factors.

[0062] This invention provides a thrust prediction system for a direct-drive feed system that considers the machining process, comprising:

[0063] The frequency characteristic acquisition unit is used to acquire the frequency characteristics of the cutting force in three directions during the machining process of the direct drive feed system;

[0064] The mechanical vibration response calculation unit is used to calculate the mechanical vibration response of the direct drive feed system under the disturbance of the obtained cutting force;

[0065] The analysis model building unit is used to calculate the servo drive current and motor air gap magnetic field considering the mechanical vibration response based on the obtained mechanical vibration response.

[0066] The thrust calculation unit is used to calculate the linear motor thrust considering the machining process based on the servo drive current and the motor air gap magnetic field that take into account the mechanical vibration response.

[0067] The prediction unit is used to predict the thrust of the direct drive feed system based on the obtained linear motor thrust.

[0068] Implementation Cases

[0069] Specifically, a high-speed five-axis machining center driven by a linear motor was used as the implementation case. The x-axis was selected as the test object, and the tool and cutting parameters are shown in Table 1. The cutting force was measured using a Kissler 9265B dynamometer with a sampling frequency of 20kHz. The motor thrust was measured using CNC system (Heidenhain, LMP28-200-3WDE-232) monitoring software with a sampling frequency of 1kHz.

[0070] Table 1 Processing Parameters

[0071]

[0072] 1) Obtain the frequency characteristics of the cutting force in three directions during the machining process through experimental testing or theoretical calculation:

[0073]

[0074] 2) Establish a mechanical dynamics model of the direct-drive feed system and calculate the dynamic vibration response in different directions of the machine considering the cutting force disturbance:

[0075]

[0076] 3) Considering the mechanical vibration response during the processing obtained in step two, calculate the servo drive current and the motor air gap magnetic field considering the mechanical vibration response:

[0077]

[0078]

[0079] 4) Based on the servo drive current considering the influence of mechanical vibration response and the motor air gap magnetic field, the linear motor thrust considering the machining process is calculated:

[0080]

[0081] Since the performance parameters of all linear motors in the machining center are unknown, parameter identification was not carried out due to experimental limitations. Therefore, only the frequency components were verified. The corresponding frequencies were extracted, and the theoretical calculation results and experimental test results were compared, as shown in Table 2-4. The table shows that during part machining, due to the coupling effect of cutting force harmonics and the original thrust harmonics, a large number of new thrust harmonic components are indeed generated. The maximum deviation between the experimental test results and the theoretical calculation results for these frequencies is only 2.03%, proving the reliability and effectiveness of the previous thrust characteristic modeling and calculation.

[0082] Table 2 Results of the influence of the first-order cutting force harmonic on the thrust characteristics of the linear motor

[0083]

[0084] Table 3. Results of the influence of the second-order cutting force harmonic on the thrust characteristics of the linear motor.

[0085]

[0086]

[0087] Table 4. Results of the influence of the third-order cutting force harmonic on the thrust characteristics of the linear motor.

[0088]

[0089] 5) Based on the motor thrust obtained in step four, perform spectrum analysis to analyze the main sources of thrust harmonics in the direct drive feed system during the machining process, and obtain the following results:

[0090] F mc (t)=F0(t)+F r (t)+F ce (t)+F cag (t)+F cee (t)+F cother (t)

[0091] Based on the frequency distribution of each harmonic, the thrust harmonics of the direct drive feed system during machining mainly come from five aspects: first, low-frequency fluctuations caused by the nonlinearity of the original drive circuit and the nonlinearity of the motor structure; second, the motor adjustment thrust caused by the cutting force disturbance; third, the new thrust harmonics generated by the cutting force in the machining process by changing the air gap magnetic field; fourth, the new thrust harmonics generated by the cutting force in the machining process by affecting the drive current; and fifth, thrust harmonics caused by other factors.

[0092] Comparing the frequency characteristics of thrust considering the processing versus not considering the processing, such as Figure 3As shown, cutting force disturbances mainly affect the output thrust of the linear motor through two pathways: First, by generating feed displacement fluctuations, encoder feedback errors are generated, which, through the servo driver, couple with the existing thrust harmonics to produce new thrust harmonics. In this process, improper installation of the linear encoder can lead to non-ideal encoder errors, exacerbating the coupling phenomenon. Second, multi-frequency cutting force disturbances in three directions intensify the vibration of the mechanical components of the direct-drive feed system. The mechanical vibration with a normal component causes air gap fluctuations in the linear motor, directly generating new thrust harmonic components. Therefore, for direct-drive feed systems applied in high-speed machine tools, the structural layout should be optimized according to the machine tool's structure to reduce the impact of cutting force disturbances on the direct-drive feed system. Furthermore, based on the frequency analysis characteristics of the thrust harmonics, appropriate control strategies should be added to improve the thrust fluctuation phenomenon during machining and ensure the machining accuracy of the parts.

Claims

1. A thrust prediction method for a direct-drive feed system considering the machining process, characterized in that, Includes the following steps: Step 1: Obtain the frequency characteristics of the cutting force in the three directions during the machining process of the direct drive feed system; Step 2: Calculate the mechanical vibration response of the direct drive feed system under the disturbance of the cutting force obtained in Step 1; Step 3: Based on the mechanical vibration response obtained in Step 2, calculate the servo drive current and the air gap magnetic field of the motor considering the mechanical vibration response. Step 4: Based on the servo drive current and motor air gap magnetic field that take into account the mechanical vibration response, calculate the linear motor thrust that takes into account the machining process. Step 5: Based on the obtained linear motor thrust, predict the thrust of the direct drive feed system; In step 2, the mechanical vibration response of the direct drive feed system under the cutting force disturbance obtained in step 1 is calculated using the following formula: in, x is the vibration output vector of the mechanical system; c , y c , z c , θ cx , θ cy , θ cz These represent the linear vibrations of the mechanical system along the x, y, and z axes and the torsional vibrations about the x, y, and z axes, respectively, under the action of cutting force; x ci , ω xci , φ xci Let represent the amplitude, frequency, and phase of the i-th order linear vibration along the x-axis; y ci , ω yci , φ yci Let z represent the amplitude, frequency, and phase of the i-th order linear vibration along the y-axis; ci , ω zci , φ zci Let θ represent the amplitude, frequency, and phase of the i-th order linear vibration along the z-axis; xci ,ω θxci, φ θxci Let θ represent the amplitude, frequency, and phase of the i-th order torsional vibration about the x-axis; yci , ω θyci , φ θyci Let θ represent the amplitude, frequency, and phase of the i-th order torsional vibration about the y-axis; zci , ω θzci , φ θzci These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the z-axis, respectively. In step 3, based on the mechanical vibration response obtained in step 2, the servo drive current and the motor air gap magnetic field considering the mechanical vibration response are calculated. The specific method is as follows: Among them, i a (t),i b (t),i c (t) represents the output current of the three phases a, b, and c of the drive circuit, respectively; t is time; I am ,I bm ,I cm Let fm be the amplitudes of the m-th order current harmonics of phases a, b, and c, respectively; f0 be the current frequency; I ... ri ,f ri ,γ ri Let B represent the amplitude, frequency, and phase of the i-th order current input harmonic caused by mechanical vibration; a (x),B b (x),B c (x) represents the a, b, and c components of the air gap magnetic field distribution of the permanent magnet considering mechanical vibration; x is the coordinate of the permanent magnet stator coordinate system; λ r (x,t) and λ p (x,t) are the equivalent relative magnetic permeability functions for mechanical roll and pitch vibrations, respectively; B ma (x),B mb (x),B mc (x) represents the a, b, and c components of the air gap magnetic field distribution of the permanent magnet, respectively; ω is the angular frequency of the motor. In step 4, the linear motor thrust considering the machining process is calculated using the following formula: Among them, F mc (t) represents the motor thrust considering the machining process; v is the feed rate; L a , L b , L c These are the self-inductances of the three-phase coils of the motor; M ab M ac M bc These represent the mutual inductance of the three-phase coils of the motor; N is the number of coil turns; l is the coil width; and τ is the motor pole pitch.

2. The thrust prediction method for a direct-drive feed system considering the machining process according to claim 1, characterized in that, In step 1, the specific expression for the frequency characteristics of the cutting force in the three directions during machining of the direct drive feed system is: Among them, F cxj , ω cxj , φ cxj These represent the amplitude, frequency, and phase of the j-th order cutting force component along the x-axis; F cyj ,ω cyj , φ cyj These represent the amplitude, frequency, and phase of the j-th order cutting force component along the y-axis; F czj , ω czj , φ czj These represent the amplitude, frequency, and phase of the j-th order cutting force component along the z-axis.

3. The thrust prediction method for a direct-drive feed system considering the machining process according to claim 1, characterized in that, In step 5, the thrust of the direct-drive feed system is predicted based on the obtained linear motor thrust. The specific method is as follows: The obtained motor thrust is subjected to spectral analysis to predict the thrust of the direct drive feed system considering the machining process. The obtained thrust of the direct drive feed system considering the machining process is shown in the following formula: Among them, F mc F(t) represents the motor thrust considering the machining process; F0(t) represents the nominal motor thrust; F r (t) represents the nominal thrust harmonics of the motor; F ce (t) represents the adjusting thrust generated by the cutting force during the machining process; F cag (t) represents the coupled thrust generated during the cutting process via the motor air gap; F cee (t) represents the coupled thrust generated during the cutting process via closed-loop feedback; F cother (t) represents the new impetus generated by other factors.

4. A thrust prediction system for a direct-drive feed system considering the machining process, characterized in that, Based on the prediction method of claim 1, the system comprises: The frequency characteristic acquisition unit is used to acquire the frequency characteristics of the cutting force in three directions during the machining process of the direct drive feed system; The mechanical vibration response calculation unit is used to calculate the mechanical vibration response of the direct drive feed system under the disturbance of the obtained cutting force; The analysis model building unit is used to calculate the servo drive current and motor air gap magnetic field considering the mechanical vibration response based on the obtained mechanical vibration response. The thrust calculation unit is used to calculate the linear motor thrust considering the machining process based on the servo drive current and the motor air gap magnetic field that take into account the mechanical vibration response. The prediction unit is used to predict the thrust of the direct drive feed system based on the obtained linear motor thrust.

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