A method and system for predicting displacement fluctuations in a direct-drive feed system considering the machining process.

Abstract

This invention provides a method and system for predicting displacement fluctuations in a direct-drive feed system considering the machining process, comprising the following steps: Step 1, acquiring the spectral characteristics of the cutting force and the linear motor thrust during the machining process; Step 2, calculating the mechanical vibration output response of the direct-drive feed system under the action of the cutting force and the linear motor thrust; Step 3, constructing a coupled integrated model of the direct-drive feed system considering the cutting force disturbance based on the mechanical vibration output response obtained in Step 2; Step 4, predicting the displacement fluctuations of the direct-drive feed system considering the machining process based on the obtained coupled integrated model of the direct-drive feed system considering the cutting force disturbance. This invention can achieve accurate prediction of displacement fluctuations in a direct-drive feed system considering the part machining process, revealing the influence of the machining process on the electromechanical coupling phenomenon of the feed system, and is of great significance for the analysis of the causes of motion errors in direct-drive feed systems, as well as further structural optimization and control compensation.

Description

Technical Field

[0001] This invention belongs to the field of drive and transmission technology, specifically relating to a method and system for predicting displacement fluctuations in a direct drive feed system that takes into account the machining process. Background Technology

[0002] Direct-drive feed systems eliminate all intermediate mechanical transmission links, achieving "zero transmission" in feed motion. Compared to traditional ball screw and rack and pinion transmission systems, they offer advantages such as simple structure, high rigidity, high feed speed, and good motion performance, making them promising for high-speed CNC machine tools. However, without the buffer of transmission links, the motor mover and drive components are directly connected, exacerbating the complex coupling between the servo drive system and the mechanical transmission system, resulting in significant displacement fluctuations. Extensive research has shown that displacement fluctuations in the feed system directly affect the machining accuracy and surface quality of parts. Especially during the machining of complex parts, multi-frequency cutting force disturbances further aggravate these displacement fluctuations.

[0003] Current research and analysis on part machining processes mainly focus on modeling the cutting force itself, optimizing machining parameters, and the excitation effect of the cutting force on the mechanical system. For ball screw feed systems, attention has begun to be paid to the coupling effect between the feed system and the cutting process. However, insufficient attention has been paid to the complex electromechanical coupling problems in direct-drive feed systems. Related modeling and analysis work has neglected the influence of the machining process on the electromechanical coupling effect of the feed system, resulting in significant errors between theoretical calculations and actual values ​​of feed system displacement fluctuations during direct-drive machining. This makes it difficult to accurately predict its motion performance and fails to provide effective guidance for machine tool structure design and motion control compensation, thus hindering the widespread application and promotion of direct-drive feed systems in high-speed machine tools. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for predicting displacement fluctuations in a direct-drive feed system that takes into account the machining process, thereby solving the problem of large prediction errors in the motion performance prediction of direct-drive feed systems during actual part machining in the prior art, and revealing the influence mechanism of the machining process on the displacement fluctuations of the direct-drive feed system.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This invention provides a method for predicting displacement fluctuations in a direct-drive feed system that takes into account the machining process, comprising the following steps:

[0007] Step 1: Obtain the spectral characteristics of the cutting force and the linear motor thrust during the machining process, respectively;

[0008] Step 2: Calculate the mechanical vibration output response of the direct drive feed system under the action of cutting force and linear motor thrust;

[0009] Step 3: Based on the mechanical vibration output response obtained in Step 2, construct a coupled integrated model of the direct drive feed system considering cutting force disturbance;

[0010] Step 4: Based on the obtained coupled integrated model of the direct drive feed system considering cutting force disturbance, predict the displacement fluctuation of the direct drive feed system considering the machining process.

[0011] Preferably, in step 1, the spectral characteristics of the cutting force along different directions during the machining process are as follows:

[0012]

[0013] 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.

[0014] Preferably, in step 1, the spectral characteristics of the linear motor thrust are:

[0015]

[0016] Among them, F m (t) represents the motor thrust; v is the feed speed, and 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.

[0017] Preferably, in step 2, based on the mechanical structure of the direct-drive feed system, the mechanical vibration output response of the direct-drive feed system under the action of cutting force and linear motor thrust is calculated using the following formula:

[0018]

[0019] Where, x m ,y m ,z m,θ mx ,θ my ,θ mz 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 thrust of the electric motor; 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 mi ,ω xmi , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the x-axis under the action of motor thrust; y mi ,ω ymi , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the y-axis under the action of motor thrust; z mi ,ω zmi , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the z-axis under the action of motor thrust; θ xmi ,ω θxmi , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the x-axis under the action of motor thrust; θ ymi ,ω θymi , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the y-axis under the action of motor thrust; θ zmi ,ω θzmi , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the z-axis under the action of motor thrust; x ci ,ω xci , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the x-axis under the action of cutting force; y ci ,ω yci , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the y-axis under the action of cutting force; z ci ,ω zci , θ represents the amplitude, frequency, and phase of the i-th order linear vibration along the z-axis under the action of cutting force; xci ,ω θxci , Let θ represent the amplitude, frequency, and phase of the i-th order torsional vibration about the x-axis under the action of cutting force; yci ,ω θyci , θ represents the amplitude, frequency, and phase of the i-th order torsional vibration about the y-axis under the action of cutting force; zci ,ω θzci , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the z-axis under the action of cutting force.

[0020] Preferably, in step 3, the expression for the coupled integrated model of the direct-drive feed system considering cutting force disturbance, constructed based on the mechanical vibration output response obtained in step 2, is:

[0021]

[0022] Where u represents the three coordinate directions x, y, z, and F cuj ,ω cuj , Let Lp be the amplitude, frequency, and phase of the j-th order cutting force component along the u-axis, Mp1 and Mp2 be the mutual inductances between the p-phase coil and the other two phase coils, ip(t) be the p-phase coil current, p represent the three phases a, b, and c, Bp be the p-phase component of the motor air gap magnetic field distribution, Bpm be the p-phase component of the permanent magnet magnetic field distribution, Ipn be the amplitude of the nth harmonic current of the p-phase coil, M, C, and K be the inertia matrix, damping matrix, and stiffness matrix of the direct-drive mechanical system, and X be the vibration output vector of the mechanical system. and These are the first and second derivatives of X, respectively; H c F is the cutting force transmission matrix; c H is the three-dimensional vector of the cutting force. m λ is the thrust transfer matrix of the electric motor; m (x,t) is the equivalent relative permeability function of the mechanical vibration; I mq f mq ,γ mq These represent the amplitude, frequency, and phase of the qth harmonic of the drive circuit generated by mechanical vibration.

[0023] A displacement fluctuation prediction system for a direct-drive feed system considering the machining process includes:

[0024] The spectrum feature acquisition unit is used to acquire the spectrum features of the cutting force and the linear motor thrust during the machining process, respectively.

[0025] The mechanical vibration output response calculation unit is used to calculate the mechanical vibration output response of the direct drive feed system under the action of cutting force and linear motor thrust;

[0026] The model building unit is used to construct a coupled integrated model of the direct drive feed system considering cutting force disturbance based on the obtained mechanical vibration output response;

[0027] The prediction unit is used to predict the displacement fluctuation of the direct drive feed system considering the machining process, based on the obtained coupled integrated model of the direct drive feed system considering cutting force disturbance.

[0028] Compared with the prior art, the present invention has the following beneficial technical effects:

[0029] The proposed method for predicting displacement fluctuations in a direct-drive feed system considering the machining process analyzes the influence of multi-frequency cutting forces on the feed system during part machining. It constructs a coupled integrated analysis model of the direct-drive feed system considering the machining process, characterizing the displacement fluctuations of the feed system under the influence of cutting force disturbances. This improves the characterization and calculation method of motion errors in the direct-drive feed system during part machining. This method can achieve accurate prediction of displacement fluctuations in a direct-drive feed system considering the part machining process, revealing the influence of the machining process on the electromechanical coupling phenomenon of the feed system. It is of great significance for the analysis of the causes of motion errors in direct-drive feed systems, as well as for further structural optimization and control compensation. Attached Figure Description

[0030] Figure 1 It is a process for predicting displacement fluctuations in a direct-drive feed system during the machining process;

[0031] Figure 2 These are the time-domain and frequency-domain test results of the cutting force along different directions;

[0032] Figure 3 It is a coupled integrated model of a direct drive feed system that takes into account cutting force disturbances;

[0033] Figure 4 This is the result of a spectrum analysis of displacement fluctuations in a direct-drive feed system considering the machining process. Detailed Implementation

[0034] 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.

[0035] This invention provides a method for predicting displacement fluctuations in a direct-drive feed system that takes into account the machining process, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0036] Step 1: Obtain the spectral characteristics of cutting force and linear motor thrust during the machining process through theoretical calculations or experimental tests;

[0037] Spectral characteristics of cutting force along different directions:

[0038]

[0039] 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.

[0040] Spectral characteristics of linear motor thrust:

[0041]

[0042] Among them, F m (t) represents the motor thrust; v is the feed speed, and 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, where N is the number of coil turns, l is the coil width, and τ is the motor pole pitch.

[0043] Step 2: Based on the mechanical structure of the direct drive feed system, calculate the mechanical vibration output response under the motor thrust and cutting force obtained in Step 1:

[0044]

[0045] Where, x m ,y m ,z m ,θ mx ,θ my ,θ mz 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 thrust of the electric motor; 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 mi ,ω xmi , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the x-axis under the action of motor thrust; y mi ,ω ymi , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the y-axis under the action of motor thrust; z mi ,ωzmi , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the z-axis under the action of motor thrust; θ xmi ,ω θxmi , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the x-axis under the action of motor thrust; θ ymi ,ω θymi , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the y-axis under the action of motor thrust; θ zmi ,ω θzmi , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the z-axis under the action of motor thrust; x ci ,ω xci , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the x-axis under the action of cutting force; y ci ,ω yci , These represent the amplitude, frequency, and phase of the i-th order linear vibration along the y-axis under the action of cutting force; z ci ,ω zci , θ represents the amplitude, frequency, and phase of the i-th order linear vibration along the z-axis under the action of cutting force; xci ,ω θxci , Let θ represent the amplitude, frequency, and phase of the i-th order torsional vibration about the x-axis under the action of cutting force; yci ,ω θyci , θ represents the amplitude, frequency, and phase of the i-th order torsional vibration about the y-axis under the action of cutting force; zci ,ω θzci , These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the z-axis under the action of cutting force.

[0046] Step 3: Based on the mechanical vibration output response obtained in Step 2, analyze the electromechanical coupling phenomenon of the direct drive feed system during machining, and construct a coupled integrated model of the direct drive feed system considering cutting force disturbances:

[0047]

[0048] Where u represents the three coordinate directions x, y, z, and F cuj ,ω cuj , Let Lp be the amplitude, frequency, and phase of the j-th order cutting force component along the u-axis, Mp1 and Mp2 be the mutual inductances between the p-phase coil and the other two phase coils, ip(t) be the p-phase coil current, p represent the three phases a, b, and c, Bp be the p-phase component of the motor air gap magnetic field distribution, Bpm be the p-phase component of the permanent magnet magnetic field distribution, Ipn be the amplitude of the nth harmonic current of the p-phase coil, M, C, and K be the inertia matrix, damping matrix, and stiffness matrix of the direct-drive mechanical system, and X be the vibration output vector of the mechanical system. and Let X be the first and second derivatives of X, respectively; Hc be the cutting force transmission matrix; Fc be the three-dimensional vector of the cutting force; Hm be the motor thrust transmission matrix; λm(x,t) be the equivalent relative permeability function of the mechanical vibration; and Imq, fmq, and γmq be the amplitude, frequency, and phase of the qth harmonic of the driving circuit generated by the mechanical vibration, respectively.

[0049] Step 4: Based on the coupled integration model in Step 3, calculate the mechanical vibration output response of the direct drive feed system considering the machining process, and extract the mechanical vibration response in the feed direction, which is the displacement fluctuation of the system.

[0050] Spectral analysis of system displacement fluctuations is performed, and the main causes of motion errors are analyzed based on the frequency distribution of different harmonic components.

[0051] The present invention also provides a displacement fluctuation prediction system for a direct-drive feed system that takes into account the machining process, comprising:

[0052] The spectrum feature acquisition unit is used to acquire the spectrum features of the cutting force and the linear motor thrust during the machining process, respectively.

[0053] The mechanical vibration output response calculation unit is used to calculate the mechanical vibration output response of the direct drive feed system under the action of cutting force and linear motor thrust;

[0054] The model building unit is used to construct a coupled integrated model of the direct drive feed system considering cutting force disturbance based on the obtained mechanical vibration output response;

[0055] The prediction unit is used to predict the displacement fluctuation of the direct drive feed system considering the machining process, based on the obtained coupled integrated model of the direct drive feed system considering cutting force disturbance.

[0056] Implementation Cases

[0057] 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, and the motor thrust and output displacement of the feed system were measured using CNC system (Heidenhain, LMP28-200-3WDE-232) monitoring software.

[0058] Table 1 Processing Parameters

[0059]

[0060] 1) Obtain the spectral characteristics of cutting force and linear motor thrust during the machining process through experimental testing;

[0061] The spectral characteristics of cutting force along different directions are as follows: Figure 2 As shown, that is:

[0062]

[0063] The spectral characteristics of the thrust of the linear motor, and its main frequency components are shown in Table 3, namely:

[0064]

[0065] Table 3 Main thrust harmonic components of linear motors

[0066]

[0067] 2) Based on the mechanical structure of the direct drive feed system, calculate the mechanical vibration output response under the action of motor thrust and cutting force:

[0068]

[0069] 3) Based on the mechanical vibration response obtained in step two, analyze the electromechanical coupling phenomenon of the direct-drive feed system during the machining process, such as... Figure 3 As shown, a coupled integrated model of the direct drive feed system considering cutting force disturbance is constructed, i.e.

[0070]

[0071] Step 4: Calculate the displacement fluctuation of the direct drive feed system considering the machining process. The time domain and frequency domain results are as follows: Figure 4 As shown. By Figure 4It can be seen that during the machining process, due to the disturbance of the cutting force, feed displacement fluctuations with the same frequency as the cutting force harmonics will occur, and the root mean square value of the displacement fluctuation is about 2.6 micrometers. According to the frequency distribution of each harmonic, the displacement fluctuation of the feed system mainly comes from four aspects: first, low-frequency fluctuations caused by the nonlinearity of the original drive circuit and the nonlinearity of the motor structure; second, displacement fluctuations caused by the cutting force disturbance; third, the machining process aggravates the electromechanical coupling problem of the system, generating new coupling thrusts on both sides of the cutting force frequency, ultimately causing corresponding displacement fluctuations; and fourth, during the machining process, the multi-frequency excitation of the cutting force will excite the vibration modes of the CNC machine tool and other components, which will lead to displacement fluctuations.

Claims

1. A method for predicting displacement fluctuations in a direct-drive feed system considering the machining process, characterized in that, Includes the following steps: Step 1: Obtain the spectral characteristics of the cutting force and the linear motor thrust during the machining process, respectively; Step 2: Calculate the mechanical vibration output response of the direct drive feed system under the action of cutting force and linear motor thrust; Step 3: Based on the mechanical vibration output response obtained in Step 2, construct a coupled integrated model of the direct drive feed system considering cutting force disturbance; Step 4: Based on the obtained coupled integrated model of the direct drive feed system considering cutting force disturbance, predict the displacement fluctuation of the direct drive feed system considering the machining process. In step 2, based on the mechanical structure of the direct drive feed system, the mechanical vibration output response of the direct drive feed system under the action of cutting force and linear motor thrust is calculated using the following formula: Where, x m , y m , z m , θ mx , θ my , θ mz 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 thrust of the electric motor; 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 mi , ω xmi , φ xmi These represent the amplitude, frequency, and phase of the i-th order linear vibration along the x-axis under the action of motor thrust; y mi , ω ymi , φ ymi These represent the amplitude, frequency, and phase of the i-th order linear vibration along the y-axis under the action of motor thrust; z mi , ω zmi , φ zmi These represent the amplitude, frequency, and phase of the i-th order linear vibration along the z-axis under the action of motor thrust; θ xmi , ω θxmi , φ θxmi These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the x-axis under the action of motor thrust; θ ymi , ω θymi , φ θymi These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the y-axis under the action of motor thrust; θ zmi , ω θzmi , φ θzmi These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the z-axis under the action of motor thrust; x ci , ω xci , φ xci These represent the amplitude, frequency, and phase of the i-th order linear vibration along the x-axis under the action of cutting force; y ci , ω yci , φ yci These represent the amplitude, frequency, and phase of the i-th order linear vibration along the y-axis under the action of cutting force; z ci ,ω zci , φ zci θ represents the amplitude, frequency, and phase of the i-th order linear vibration along the z-axis under the action of cutting force; xci , ω θxci ,φ θxci θ represents the amplitude, frequency, and phase of the i-th order torsional vibration about the x-axis under the action of cutting force; yci , ω θyci , φ θyci θ represents the amplitude, frequency, and phase of the i-th order torsional vibration about the y-axis under the action of cutting force; zci , ω θzci , φ θzci These represent the amplitude, frequency, and phase of the i-th order torsional vibration about the z-axis under the action of cutting force. In step 3, the expression for the coupled integrated model of the direct drive feed system considering cutting force disturbance, constructed based on the mechanical vibration output response obtained in step 2, is as follows: Where u represents the three coordinate directions x, y, z, and F cuj , ω cuj , φ cuj Let be the amplitude, frequency, and phase of the j-th order cutting force component along the u-axis; m be the three phases a, b, and c; M, C, and K be the inertia matrix, damping matrix, and stiffness matrix of the direct-drive mechanical system; X be the vibration output vector of the mechanical system; H be the amplitude, frequency, and phase of the j-th order cutting force component along the u-axis; H be the amplitude, frequency, and phase of the j-th order cutting force component along the u-axis; M ... c F is the cutting force transmission matrix; c H is the three-dimensional vector of the cutting force. m λ is the thrust transfer matrix of the electric motor; m (x,t) is the equivalent relative permeability function of the mechanical vibration; I mq f mq ,γ mq These represent the amplitude, frequency, and phase of the qth harmonic of the drive circuit generated by mechanical vibration.

2. The method for predicting displacement fluctuations in a direct-drive feed system considering the machining process according to claim 1, characterized in that, In step 1, the spectral characteristics of the cutting force along different directions during the machining process are as follows: 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 method for predicting displacement fluctuations in a direct-drive feed system considering the machining process according to claim 1, characterized in that, In step 1, the spectral characteristics of the linear motor thrust are as follows: Among them, F m (t) represents the motor thrust; v is the feed speed, and 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.

4. A displacement fluctuation prediction system for a direct-drive feed system considering the machining process, characterized in that, The prediction method based on claim 1 includes: The spectrum feature acquisition unit is used to acquire the spectrum features of the cutting force and the linear motor thrust during the machining process, respectively. The mechanical vibration output response calculation unit is used to calculate the mechanical vibration output response of the direct drive feed system under the action of cutting force and linear motor thrust; The model building unit is used to construct a coupled integrated model of the direct drive feed system considering cutting force disturbance based on the obtained mechanical vibration output response; The prediction unit is used to predict the displacement fluctuation of the direct drive feed system considering the machining process, based on the obtained coupled integrated model of the direct drive feed system considering cutting force disturbance.

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