A Microstructure Profile Prediction and Pre-Compensation Machining Method

Abstract

The present invention discloses a method for predicting and pre-compensating the micro-structure profile, comprising the following steps: establishing a servo control model; establishing a cutting force model and obtaining a transfer function of the cutting force and the generated displacement; adding the cutting force model into the servo control model to obtain a coupled model of the cutting system and the servo system and obtaining a transfer function of the theoretical position command and the tool tip position; determining the theoretical input of the machine tool linear axis, obtaining the tool tip output trajectory through the coupled model and considering the repeat positioning error, and obtaining the prediction and compensation result of the micro-structure profile error. Based on the disturbance effect of the variable cutting force on the servo system itself in micro-structure machining, compared with the traditional research method without cutting force disturbance, the method is closer to the experimental result by adopting a force-displacement-vibration coupled servo model, thereby making the prediction accuracy of the ultra-precision machine tool machining profile higher.

Description

Technical Field

[0001] The present invention relates to the field of ultra-precision machining technology, and particularly relates to a micro-structure profile prediction and pre-compensation machining method. Background Art

[0002] Many organisms in nature have complex macroscopic surface shapes. A series of studies on biological surfaces have been carried out by many researchers, and it has been found that there are micron- and sub-micron-scale micro-structures on the surface, which is also an important reason for their special properties. With the continuous development of technology, the special properties of micro-structures are widely applied in the fields of electronics, communication, optics, avionics, medical treatment, and automobiles. The ultra-precision single-point diamond lathe is widely regarded as one of the key core equipments for realizing the preparation of micro-structures. Through the orthogonal slow tool servo machining process, various micro-structures with different wave patterns and grooves can be machined on the ultra-precision single-point diamond lathe.

[0003] The machining accuracy of micro-structures is the key factor for the quality of the special properties of micro-structures. In an ideal situation, micro-structures that conform to the design can be machined according to the designed orthogonal slow tool servo machining program. However, there must be errors in the ultra-precision single-point diamond lathe, which will inevitably lead to the inconsistency between the machining accuracy of the micro-structures and the design, that is, there is a machining profile error.

[0004] The servo control system is the core of the ultra-precision single-point diamond lathe. The servo control accuracy of the system, as a key technical index of the ultra-precision machine tool, directly affects the preparation accuracy of the micro-structures of the ultra-precision machine tool. Since the slow tool servo machining of micro-structures on the ultra-precision machine tool can achieve a sub-micron-level profile error, any disturbance to the servo control system will cause a loss of the machining accuracy of the workpiece, thereby further affecting the application performance of the micro-structures. The cutting force is one of the inevitable disturbances in the process of micro-structure machining, and the cutting force during the ultra-precision machining of micro-structures has the characteristics of high-frequency periodicity and large change in the cutting force amplitude, which introduces unknown disturbance characteristics to the low-bandwidth servo control system of the ultra-precision feed axis. Moreover, the spindle for installing the workpiece in the ultra-precision machine tool is an air-bearing spindle, unlike the spindle of a general machine tool which is a mechanical structure. Therefore, the spindle stiffness of the ultra-precision machine tool is weaker, and the influence of the cutting force on the weak-stiffness spindle must be considered.

[0005] Error compensation methods are one of the effective means to improve machining accuracy. However, the prerequisite for compensation is to accurately know the characteristics of the error. Therefore, predicting the machining profile error of microstructures and carrying out compensation work are important tasks in the ultra-precision machining of microstructures. The current prediction methods mainly include: obtaining the transfer function of the servo tracking error by fitting the step response test, and then carrying out the machining accuracy modeling of microstructures; establishing a control system according to the controller used in the machine tool, calculating the servo tracking error, and further analyzing the influence on machining accuracy. Existing research is based on the PD-type tracking error prediction model, considering the error generated by tool interpolation, and establishing an accuracy prediction model. To sum up, the current research obtains the tracking error identification and prediction model through the fitting of high-order functions and the modeling of the machine tool hardware control module, and further establishes the contour prediction model based on the tracking error identification and prediction model. The cutting force that inevitably exists in the machining of microstructures is not considered, resulting in a significant difference between the contour prediction and the actual machining process, and it cannot be used for error compensation.

[0006] The machining cutting force has been considered and analyzed in the conventional milling process, mainly focusing on the analysis of cutting force magnitude, tool wear research, chatter analysis research, etc. Due to the excellent anti-disturbance ability of the lead screw and guide rail drive structure, the cutting force has no fundamental impact on the servo control system in conventional machining. However, in the ultra-precision machining of microstructures, the cutting force transmission process is significantly different from the existing machining scenarios that consider cutting force, so the influence of cutting force on the servo control system cannot be ignored.

[0007] To sum up, the contour error prediction model considering cutting force designed in this invention patent is a necessary and original work to improve the accuracy of ultra-precision machining of microstructures. Summary of the Invention

[0008] The purpose of the present invention is to: aiming at the problem that the interference of cutting force on the servo control system in the actual machining conditions is not considered in the existing research on microstructure machining, which leads to inaccurate prediction of the machining contour of ultra-precision machine tools, a microstructure contour prediction and pre-compensation machining method is provided. This method is based on the research on the interference mechanism of cutting force on the servo control system and establishes a coupling model, making the prediction of the microstructure contour more accurate.

[0009] The present invention is realized through the following technical solutions:

[0010] The present invention provides a microstructure contour prediction and pre-compensation machining method, including the following steps:

[0011] Establish a servo control model;

[0012] Establish a cutting force model and obtain the transfer function of the cutting force and the generated displacement;

[0013] The cutting force model is incorporated into the servo control model to obtain the coupled model of the cutting system and the servo system, and the transfer function between the theoretical position command and the tool tip position is obtained;

[0014] Determine the theoretical input of the machine tool linear axis. Through the coupled model and considering the repeat positioning error, the tool tip output trajectory is obtained, and the prediction and compensation results of the micro-structure profile error are obtained.

[0015] In some embodiments, according to the controller used in the ultra-precision machine tool and combined with the actual use of the function modules of the ultra-precision machine tool control system, a servo control model is established.

[0016] In some embodiments, establishing the cutting force model includes the following steps:

[0017] Establish an input-output trajectory value expression considering the multi-error model:

[0018] X2(s) = X in (s)G2(s)

[0019] where X in is the theoretical position command, and X2 is the actual output signal of the tool tip;

[0020] Establish the cutting force formula:

[0021] F(t) = Kb(t)h(t)

[0022] where F(t) represents the cutting force at time t, b(t) is the variable cutting width, K is the cutting force coefficient related to the workpiece material, and h(t) is the depth of cut at the current moment;

[0023] The variable depth of cut is expressed as:

[0024] h(t) = z(t) - z(t - ε)

[0025] where z(t) is the displacement caused by the actual cutting force, and ε is the time interval;

[0026] The variable cutting width b(t) is expressed as:

[0027] b(t) = x(t) - x(t - ε1)

[0028] where x(t) is the motion trajectory of the X-axis during machining, and ε1 is the time interval.

[0029] In some embodiments, the transfer function G t (s) of the cutting force F of the tool and the generated displacement Z1 is:

[0030]

[0031] where, m1 is the equivalent mass of the tool rest model, k1 is the equivalent stiffness of the tool rest model, and c1 is the equivalent damping of the tool rest model.

[0032] In some embodiments, the transfer function G of the cutting force and displacement of the spindle is obtained w as:

[0033]

[0034] where m w is the equivalent mass of the spindle model, k w is the equivalent stiffness of the spindle model, and c w is the equivalent damping of the spindle model.

[0035] In some embodiments, an expression for the relative vibration z3 between the tool and the workpiece generated by the servo system of the ultra-precision lathe is established:

[0036] z3(s) = F(s)G t (s) - F(s)G w (s)

[0037] In some embodiments, according to the coupling model, a simulation model of the relative vibration between the tool and the workpiece caused by the cutting force is solved, and an expression for the machining surface profile of the planar part is established by integrating various factors:

[0038] X2(t) = E1 + Z act (t) + Z3(t)

[0039] where X2(t) is the tool output trajectory considering external environmental vibration, E1 is the repeat positioning error, and Z act (s) is the output of the machine tool guide rail.

[0040] In some embodiments, the high-order transfer function G2(s) of the theoretical position command and the tool tip position is obtained as:

[0041]

[0042] where X in is the theoretical position command, and X2 is the actual output signal of the tool tip.

[0043] In some embodiments, by comparing the micro-structure profile obtained from the tool tip trajectory according to the mapping relationship with the ideal micro-structure profile, the profile error of the micro-structure can be obtained.

[0044] In some embodiments, obtaining the prediction and compensation results of the micro-structure profile error includes the following steps:

[0045] Predicting the profile error after machining by the prediction model;

[0046] Determine the input trajectory after the linear axis pre-compensation of the machine tool, and calculate the actual output position;

[0047] Calculate the contour error after pre-compensation, and after N iterations, when the maximum contour error value is less than the target allowable maximum contour error, determine the iterative pre-compensation value.

[0048] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0049] Based on the research on the interference mechanism of cutting force on the servo control system, the present invention establishes a coupling model of cutting force and servo system. During the micro-structure cutting process, due to the changes in cutting depth and feed rate, the variable cutting force also inevitably disturbs the servo system itself. The output displacement of the servo control system acts on the tool tip point through mechanical transmission, affecting the output position of the tool tip point, and in turn, reversely affecting the magnitude of the cutting force. There is a coupling relationship between the two. Therefore, according to the servo control system modeling method of ultra-precision machine tools, it is very important to establish a variable cutting force model during machining and study the interference mechanism of cutting force on the servo control system. Compared with the traditional modeling method without cutting force disturbance research, the force-displacement-vibration coupling servo model is closer to the experimental results, further verifying the accuracy of the analysis of the disturbance law of cutting force on the machine tool motion trajectory and tracking error, thus making the prediction of the machining contour of ultra-precision machine tools more accurate. After error compensation by the compensation method, the contour error of micro-structure ultra-precision machining is smaller and closer to the designed micro-structure. Description of the Drawings

[0050] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the drawings required for the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings. In the drawings:

[0051] Figure 1 It is the overall research block diagram of the force-displacement-vibration coupling servo model in the present invention;

[0052] Figure 2 It is the cutting force model in the present invention;

[0053] Figure 3 It is the tool dynamics model during the machining process in the present invention;

[0054] Figure 4 It is the dynamics model of the ultra-precision turning tool and the workpiece surface in the present invention;

[0055] Figure 5The simulation diagram of the relative vibration between the tool and the workpiece caused by the cutting force in the servo system of the present invention;

[0056] Figure 6 The coupling model of the cutting system and the servo system of the present invention;

[0057] Figure 7 The comparison diagram of the Z-axis trajectory and tracking error simulation results of the two models of the present invention;

[0058] Figure 8 The cutting force simulation result of the present invention;

[0059] Figure 9(a) shows the comparison result of the contour error based on the force-coupled contour prediction model of the present invention;

[0060] Figure 9(b) shows the comparison result of the contour error based on the traditional contour prediction model of the present invention;

[0061] Figure 10 The contour error multi-iteration pre-compensation model of the present invention;

[0062] Figure 11 The comparison diagram of the microstructure contour before and after error compensation in the present invention. Detailed implementation manners

[0063] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the embodiments and the accompanying drawings. The illustrative embodiments of the present invention and their descriptions are only used to explain the present invention and do not limit the present invention.

[0064] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which this application belongs; the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit this application; the terms "including" and "having" and any variations thereof in the specification and claims of this application and the above drawings are intended to cover non-exclusive inclusion.

[0065] In the description of the embodiments of this application, technical terms such as "first" and "second" are only used to distinguish different objects and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity, specific order, or primary-secondary relationship of the indicated technical features.

[0066] References to "embodiments" in this application mean that the specific features, structures, or characteristics described in connection with the embodiments can be included in at least one embodiment of the present application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art will explicitly and implicitly understand that the embodiments described herein can be combined with other embodiments.

[0067] In the description of the embodiments of the present application, the term "and / or" is merely a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can mean: the existence of A, the simultaneous existence of A and B, and the existence of B. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0068] In the embodiments of the present application, the same reference numerals represent the same components, and for the sake of brevity, in different embodiments, the detailed description of the same components is omitted. It should be understood that the thickness, length, width, etc. of various components in the embodiments of the present application shown in the drawings, as well as the overall thickness, length, width, etc. of the integrated device, are only for illustrative purposes and should not constitute any limitation to the present application.

[0069] In the description of the embodiments of the present application, the term "plurality" refers to two or more (including two). Similarly, "multiple groups" refers to two or more groups (including two groups), and "multiple pieces" refers to two or more pieces (including two pieces), unless otherwise specifically defined.

[0070] In the description of the embodiments of the present application, the orientation or positional relationship indicated by technical terms such as "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the embodiments of the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the embodiments of the present application.

[0071] In the description of the embodiments of the present application, unless otherwise clearly specified and limited, technical terms such as "installation", "connection", "connection", "fixation", etc. should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral body; it can also be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements or the interaction relationship between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the embodiments of the present application can be understood according to specific circumstances.

[0072] In the embodiment of the present application, a tracking error identification model based on a force-displacement-vibration coupling servo model is established according to the coupling effect between the cutting force and the servo control system, and the influence law of the coupling effect relationship between the cutting force and the servo system on the tracking error of the feed axis is analyzed. Combining the repeat positioning error, which is one of the key factors affecting the contour accuracy, a contour error prediction model is established, and based on this, the influence law of the cutting force on the contour error is analyzed.

[0073] In the embodiment of the present application, a tracking error identification and prediction is established based on the force-displacement-vibration coupling servo model. The overall research block diagram of the model is as Figure 1 shown. The two ends are the theoretical output and the actual output trajectories, and the middle includes modules such as a servo control module, a motor module, grating feedback, external disturbances, repeat positioning error, and cutting force disturbances.

[0074] A microstructure contour prediction and pre-compensation machining method provided in the embodiment of the present application includes the following steps:

[0075] Establish a servo control model;

[0076] Establish a cutting force model and obtain the transfer function of the cutting force and the generated displacement;

[0077] Add the cutting force model to the servo control model to obtain a coupling model of the cutting system and the servo system, and obtain the transfer function of the theoretical position command and the tool tip position;

[0078] Determine the theoretical input of the machine tool linear axis, and through the coupling model and considering the repeat positioning error, obtain the tool tip output trajectory, and obtain the microstructure contour error prediction and compensation result.

[0079] The theoretical signal of the ultra-precision machine tool is sent to the linear motor through the controller and the driver to generate a driving force, which drives the movement of the machine tool linear axis. The position signal is collected through the grating for feedback, and the real-time dynamic tracking error is further calculated. In this embodiment, the PMAC controller is used for the research of the machine tool, and a servo control model is established in combination with the actual use of the function modules of the machine tool control system. The controller outputs a voltage signal, which is transmitted to the driver. The driver converts it into a current signal, and the current loop outputs a driving force through the linear motor model to drive the movement of the machine tool linear axis guide rail. It should be noted that the ultra-precision machine tool uses a permanent magnet synchronous linear motor, and the linear motor model is an existing model.

[0080] In this embodiment, establishing the cutting force model includes the following steps:

[0081] Since the tool holder is fixedly connected to the machine tool moving platform through bolts, the transfer function is almost equal to 1, and the displacement of the moving platform is approximately regarded as the actual output displacement of the tool tip point. In the slow tool servo machining of microstructures on ultra-precision machine tools, the linear axis of the machine tool needs to reciprocate. Therefore, the repeat positioning error E1 generated by the linear axis of the machine tool during machining also needs to be considered in the contour prediction model. This error can be obtained during the performance detection of ultra-precision machine tools and is a fixed error value, with a numerical value of approximately 0.2 μm. Therefore, the input-output trajectory value expression considering the multi-error model is as follows:

[0082] X2(s) = X in (s)G2(s)

[0083] where, X in is the theoretical position command, and X2 is the actual output signal of the tool tip point;

[0084] The cutting force during the machining process can be obtained according to the empirical formula. The established empirical formula for the cutting force is:

[0085] F(t) = Kb(t)h(t)

[0086] where, F(t) represents the cutting force at time t; b(t) is the variable cutting width, which is the feed per unit time during machining; K is the cutting force coefficient related to the workpiece material, obtained through a large number of experiments; h(t) is the cutting depth at the current moment;

[0087] The cutting force model is as Figure 2 shown. During the machining process, the cutting force is related not only to the theoretical cutting depth but also to the position at the current moment and the previous revolution. The variable cutting depth can be expressed as:

[0088] h(t) = z(t) - z(t - ε)

[0089] where, z(t) is the displacement caused by the actual cutting force; ε is the time interval, which is consistent with the sampling interval of the dynamometer, ε = 0.15; the variable cutting width b(t) is the change value of the displacement of the X-axis of the machine tool per unit time during machining. The variable cutting width b(t) is expressed as:

[0090] b(t) = x(t) - x(t - ε1)

[0091] where, x(t) is the motion trajectory of the X-axis extracted during machining, and ε1 is the time interval. In this embodiment, the time interval is consistent with the sampling time, and the numerical value can be 0.001 s.

[0092] During the actual machining process, the cutting force not only acts on the tool holder but also is transmitted through the force to act on the servo system, forming a coupling effect between the cutting force and the servo system. Therefore, we equivalently regard the tool holder and moving platform structure of the machine tool as a single-degree-of-freedom second-order system, and establish the tool dynamics model during the machining process asFigure 3 As shown, through Laplace transform, the transfer function G of the cutting force F of the tool and the displacement Z1 generated is derived. t (s) is:

[0093]

[0094] Where m1 is the equivalent mass of the tool rest model, k1 is the equivalent stiffness of the tool rest model, c1 is the equivalent damping of the tool rest model, and the above dynamic parameters can be obtained through experimental tests.

[0095] The relative vibration of the tool-workpiece surface generated by the coupling action of the servo system and the cutting force, based on the force-displacement-vibration coupling servo model, on the Figure 3 basis, a dynamic model of the tool and the workpiece surface is established, as Figure 4 shown, the transfer function G of the cutting force and displacement of the spindle is derived. w It is expressed as:

[0096]

[0097] Where m w is the equivalent mass of the spindle model, k w is the equivalent stiffness of the spindle model, c w is the equivalent damping of the spindle model, F represents the variable cutting force during plane part machining, and the above dynamic parameters can be obtained through experimental tests.

[0098] The variable cutting force is affected by the coupling action of the servo system. Due to the stiffness difference between the tool and the spindle, the cutting force causes different displacements of the two, resulting in mutual vibration between the tool and the workpiece. Therefore, the relative vibration z3 of the tool-workpiece generated by the servo system of the ultra-precision lathe can be expressed as:

[0099] z3(s) = F(s)G t (s) - F(s)G w (s)

[0100] Based on the force-displacement coupling servo system to solve the simulation model of the relative vibration of the tool-workpiece caused by the cutting force, as Figure 5 shown. X in (t) is the theoretical trajectory input of the Z-axis of the plane part machining machine tool, X2(t) is the tool output trajectory considering external environmental vibration, and F(t) is the cutting force calculation model. Z act (s) represents the output of the machine tool guide rail, G1(s) represents the transfer function of the motor servo control system, and considering various factors, the surface profile expression of plane part machining is established as:

[0101] X2(t) = E1 + Z act (t) + Z3(t)

[0102] Adding the cutting force model to the servo control system can obtain the coupling model of the cutting system and the servo system, as Figure 6 shown. In the figure, DesPos represents the theoretical command, and ActPos represents the actual position. The specific parameters are shown in Table 1.

[0103] Table 1 Model Parameter Table

[0104]

[0105] Substituting the parameters in Table 1, the high-order transfer function G2(s) of the theoretical position command and the tool tip position is derived as:

[0106]

[0107] where, X in is the theoretical position command, and X2 is the actual output signal of the tool tip.

[0108] In this embodiment, the force-displacement-vibration coupling servo system can accurately predict the contour error. Based on the contour prediction model, a multi-iteration pre-compensation model for contour error is established to reduce the contour error. The multi-iteration pre-compensation model for contour error is as Figure 10 shown.

[0109] Specifically, obtaining the prediction and compensation results of the microstructure contour error includes the following steps:

[0110] The contour error E P after machining by the prediction model is:

[0111] E P = X in - X2

[0112] where, X in is the theoretical position command, and X2 is the actual output signal of the tool tip;

[0113] The input trajectory X in1 after pre-compensation of the machine tool linear axis can be expressed as:

[0114] X in1 = X in - E P

[0115] After pre-compensation of the input trajectory, the actual output position X p1 (s) can be calculated as:

[0116] X p1 (s) = X in1 (s)G2(s)

[0117] = Xin (s)G2(s)-E P (s)G2(s)

[0118] The contour error after pre - compensation can be calculated as:

[0119] E p1 (s)=X in (s)-X p1 (s)

[0120] =X in (s)-X in (s)G2(s)+E P (s)G2(s)

[0121] =X in (s)-X2(s)-E P (s)G2(s)

[0122] =E P (s)-E P (s)G2(s)

[0123] =E P (s)(1 - G2(s))

[0124] It can be seen from the above formula that the contour error after pre - compensation can be reduced to 1 - G2(s) times. Existing research has found that it is difficult for the direct pre - compensation method to fully pre - compensate the large - curvature section of the curve. The perturbation error composed of small noise and some large - curvature spikes is also difficult to be fully pre - compensated. In order to further reduce the contour error, a multi - iteration pre - compensation scheme is proposed. The secondary iteration input X in2 (s) after the first pre - compensation is:

[0125] X in2 (s)=X in (s)-E P (s)-E P (s)(1 - G2(s))

[0126] The contour error E p2 (s) after the secondary iteration can be obtained as:

[0127] E p2 (s)=X in (s)-X p2 (s)

[0128] =E P (s)(1 - G2(s)) 2

[0129] Furthermore, it can be deduced that the input X inN (s) after N - times of iteration is:

[0130] X inN (s) = X in (s) - E P (s) - E P (s)(1 - G2(s)) -...... - E P (s)(1 - G2(s)) N-1

[0131] The contour error E after N iterations pN (s) is:

[0132] E pN (s) = X in (s) - X pN (s)

[0133] = E P (s)(1 - G2(s)) N

[0134] To determine the number of iterations, it is necessary to set the target allowable maximum contour error ε. After multiple iterations, when the maximum contour error value max(E pN ) < the target allowable maximum contour error ε, the iterative pre-compensation value X can be determined cN as:

[0135] X cN (s) = -E P (s) - E P (s)(1 - G2(s)) -...... - E P (s)(1 - G2(s)) N-1

[0136] The calculation result of the optimal compensation amount lays a foundation for the subsequent path planning, and the tool path calculation can be carried out based on the contour error pre-compensation amount. The compensation result is as Figure 11 shown, where part a is the microstructure contour before error compensation, and part b is the microstructure contour after error compensation. From Figure 11 it can be seen that the contour error after error compensation has been significantly reduced, and the microstructure contour has been significantly improved, further verifying the effectiveness of the real-time online error compensation method established based on the micro-nano motion platform.

[0137] In the simulation model of this embodiment, the ideal morphology is a sine microstructure, and the expression of this structure is:

[0138]

[0139] where a and b are the peak values, and λ is the sine period length.

[0140] Extract the motion trajectory of the machine tool's linear axis from the ideal three-dimensional topography according to the Archimedes spiral, as the theoretical input trajectory of the machine tool's linear axis. Since the ideal topography uses equal-angle discretization, the feed rate changes during constant-speed machining. Extract the machining trajectory of the X-axis and bring the X-axis trajectory into the simulation model. Since the X-axis motion trajectory is approximately a linear motion, the coincidence degree between the actual output trajectory and the theoretical trajectory is relatively high, and the tracking error is also very small, indicating that it is little affected by the servo system. Therefore, in the following of this embodiment, relevant analysis will be carried out for the Z-axis of the machine tool.

[0141] Figure 6 The simulation model inputs the machining motion trajectory of the Z-axis of the micro-structure, and by comparing the input and output results of the system, the prediction result of the tracking error can be obtained, as Figure 7 shown. The tracking error is larger at the peak of the trajectory, and the coincidence degree between the theoretical trajectory and the output trajectory is relatively high in the middle of the peak and valley. The tracking error during the uniform-speed process in machine tool machining is very small, and the tracking error during the acceleration and deceleration process is more prominent. As the acceleration increases, the motor torque required by the machine tool continuously increases, the saturation effect of the motor coil increases, the amplitude of the output force of the servo system increases, and the resulting tracking error is larger. In this embodiment, the simulation is carried out for the sinusoidal micro-structure. The acceleration change of the sinusoidal trajectory is still a sinusoidal trajectory, so the acceleration corresponding to the peak of the trajectory is also the maximum value, and the tracking error is larger. The position with a smaller acceleration is also in the middle of the peak, and the tracking error is smaller.

[0142] In order to further compare the superiority of the prediction model proposed in this embodiment, it is compared with the existing tracking error method. The traditional tracking error identification model is based on the motor control system to carry out tracking error identification and prediction. Substitute the motion trajectory of the sinusoidal grating to obtain the tracking error identification and prediction trajectory and error value based on the traditional model. Figure 7 Compare the simulation results of the servo control model without cutting force and the new method proposed in this embodiment respectively. The tracking error of the force-displacement-vibration coupling servo model proposed in this embodiment is larger, and the enlarged view at the peak shows the differences in the simulation results of the two methods. In order to verify and explain the reasons for this phenomenon, the comparison results of the tracking errors and the cutting force simulation results under the two methods are obtained, as Figure 8 shown.

[0143] Figure 8This is the cutting force simulation result in this embodiment. The simulation result indicates that the change of the tracking error comparison result is consistent with the change of the cutting force, demonstrating that the cutting force is the reason for the difference between the simulation results of the force-displacement-vibration coupling servo model and the traditional model. The cutting force generated at the position with an obvious change in the depth of cut is greater, which in turn leads to a larger numerical value of the tracking error obtained by the model proposed in this embodiment. The above simulation introduces the difference in the simulation results between the force-displacement-vibration coupling servo model and the traditional model in this embodiment. By comparing the results of the two methods with the simulation result of the cutting force, it further illustrates that the cutting force disturbance is the main reason for the difference from the servo control model without cutting force, and further clarifies the effect of the cutting force disturbance on the servo system.

[0144] The sine microstructure is selected as the machining object. According to the previous description, the machining trajectory is extracted along the Archimedean spiral as the theoretical input of the machine tool linear axis. After passing through the above coupling model and considering the 0.2μm repeat positioning error existing in the machine tool machining, the output trajectory of the tool tip point is obtained, and a contour prediction model is established.

[0145] The slow tool servo machining in this embodiment is a constant speed machining. From the outer edge to the center of the workpiece, the radius gradually decreases, and the linear velocity also gradually decreases. According to the formula in the cutting force model of this embodiment, the higher the linear velocity, the greater the displacement that the machine tool linear axis travels per unit time, the more the trajectory of the machine tool X-axis changes per unit time, and the more obvious the disturbance generated by the cutting force. Therefore, during the machining process from the outside to the center of the workpiece, the cutting force gradually decreases as a whole, the tracking error generated by the servo system gradually decreases, and the contour error gradually decreases from the outer circle to the center of the workpiece.

[0146] To further verify the correctness of the model, a machine tool microstructure cutting experiment was carried out. A diamond tool was used for slow tool servo machining, and the tool geometric parameters and machining parameters are shown in Table 1. The machining contour is a sine microstructure, the contour peak value is ±20μm, and the microstructure period length is 800μm. During the machine tool machining, the motion trajectory is fed back by the linear axis grating, and the controller calculates the real-time tracking error by comparing the feedback signal with its own input signal. After the machining is completed, the detected data is exported. The Kistler dynamometer is installed between the tool holder and the tool clamping seat to detect the cutting force in the direction perpendicular to the workpiece surface during the cutting process.

[0147] Comparatively analyze the input and output motion trajectories of simulation and experiment of the two methods. The tracking error is due to the phase lag of the response of the linear axis of the machine tool compared to the theoretical input value. The servo response of the linear axis of the machine tool cannot keep up with the theoretical command, resulting in a position deviation. Affected by the contour trajectory of the workpiece being machined, the tracking error is larger at positions with greater acceleration. The experimental results show that compared with the traditional modeling method, the force-displacement-vibration coupling servo model is closer to the experimental results. The experiment further verifies the accuracy of the analysis of the cause that the cutting force disturbance makes the force-displacement-vibration coupling servo model closer to the experimental results, and further verifies the accuracy of the analysis of the disturbance law of the cutting force on the motion trajectory and tracking error in the simulation.

[0148] To further verify the accuracy of the results, the contour errors of the traditional model and the force-coupled profile were respectively compared with the experiment, and the contour error comparison results were obtained, as shown in Figures 9(a) and 9(b). After comparing the contour errors of the simulation results of the non-cutting-force servo control model and the new method with the experiment in the two figures, the accuracy rates of the contour prediction results are 41.3% and 86.4% respectively. The points pointed by the arrows respectively correspond to points 1 and 2 in this embodiment Figure 8 which represent the positions corresponding to the peaks of the influence of the cutting force disturbance on the machining trajectory in the contour error. Since the influence of the cutting force disturbance is not considered in the contour error simulation of this model, there are significant differences between the non-cutting-force servo control system and the experimental results. To sum up, the experimental results show that the contour prediction model proposed in this embodiment has higher accuracy compared with the experimental results. The contour error prediction model not only accurately characterizes the structure and shape of the workpiece after machining, but also has a high consistency with the simulation in the influence law of the tracking error on the contour error.

[0149] In this embodiment, compared with the non-cutting-force servo control model, a force-displacement-vibration coupling servo model closer to the actual machining conditions is proposed. Based on this model, a tracking error prediction model is established, and the influence of the linear axis repeat positioning error is added to propose a contour prediction model. The experiment first verifies the accuracy of the variable cutting force prediction results in the force-displacement-vibration coupling servo model, and characterizes the different influences of the variable cutting force at different positions on the motion trajectory during machining. The prediction model characterizes the motion trajectory of the linear axis and the workpiece surface contour during the slow tool servo machining of microstructures on ultra-precision machine tools. By comparative analysis, the dynamic tracking error and contour error are further determined. Compared with the non-cutting-force servo control model, the accuracy rate of the prediction model is increased by 45%. Based on the analysis of the cutting machining mechanism, the influence of the cutting force on the servo system is explained, thus explaining why the force-displacement-vibration coupling servo model prediction model has higher accuracy. The causes of the tracking error and contour error are analyzed for the experimental and simulation results, revealing the influence law of the cutting force disturbance on the tracking error and contour error, laying a foundation for the subsequent error compensation of the micro-structure machining of ultra-precision machine tools and the improvement of machining accuracy.

[0150] The specific embodiments described above further elaborate on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only for the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A microstructure profile prediction and pre-compensation machining method, characterized in that It includes the following steps: Establish a servo control model; Establish a cutting force model and obtain the transfer function of the cutting force and the generated displacement; Add the cutting force model to the servo control model to obtain the coupled model of the cutting system and the servo system, and obtain the transfer function of the theoretical position command and the tool tip position; Determine the theoretical input of the machine tool linear axis, and through the coupled model and considering the repeat positioning error, obtain the tool tip output trajectory and the prediction and compensation results of the micro-structure profile error; Among them, establishing the cutting force model includes the following steps: Establish an input-output trajectory value expression considering the multi-error model: X2(s) = X in (s)G2(s) where X in is the theoretical position command, and X2 is the actual output signal of the tool tip point; Establish a cutting force formula: F(t) = Kb(t)h(t) In the formula, F(t) represents the cutting force at time t, b(t) is the variable cutting width, K is the cutting force coefficient related to the workpiece material, and h(t) is the cutting depth at the current moment; The variable cutting depth is expressed as: h(t) = z(t) - z(t - ε) In the formula, z(t) is the displacement caused by the actual cutting force, and ε is the time interval; The variable cutting width b(t) is expressed as: b(t) = x(t) - x(t - ε1) In the formula, x(t) is the motion trajectory of the X-axis during machining, and ε1 is the time interval; Among them, the transfer function G(s) for obtaining the cutting force F of the cutting tool and generating the displacement Z1 is: t (s) is: In the formula, m1 is the equivalent mass of the tool rest model, k1 is the equivalent stiffness of the tool rest model, and c1 is the equivalent damping of the tool rest model; Among them, the transfer function G for obtaining the cutting force and displacement of the main shaft w is as follows: In the formula, m w is the equivalent mass of the spindle model, k w is the equivalent stiffness of the spindle model, c w is the equivalent damping of the spindle model; Among them, establish the expression of the relative vibration z3 between the tool and the workpiece generated by the ultra-precision lathe servo system: z3(s) = F(s)G t (s) - F(s)G w (s); Among them, solve the simulation model of the relative vibration between the tool and the workpiece caused by the cutting force according to the coupled model, and establish the expression of the machining surface profile of the planar workpiece by integrating various factors: X2(t) = E1 + Z act (t) + Z3(t) where X2(t) is the tool output trajectory considering external environmental vibrations, E1 is the repeat positioning error, and Z act (s) is the output of the machine tool guideway; Among them, the high-order transfer function G2(s) of the theoretical position command and the tool tip position is: where X in is the theoretical position command, and X2 is the actual output signal of the tool tip point.

2. The microstructure profile prediction and pre-compensation machining method according to claim 1, wherein, According to the controller used in the ultra-precision machine tool and combined with the actual use of the functional modules of the ultra-precision machine tool control system, establish a servo control model.

3. The microstructure profile prediction and pre-compensation machining method according to claim 1, characterized in that By comparing the micro-structure profile obtained from the tool tip trajectory according to the mapping relationship with the ideal micro-structure profile, the profile error of the micro-structure can be obtained.

4. The microstructure profile prediction and pre-compensation machining method according to claim 1, characterized in that Obtaining the prediction and compensation results of the micro-structure profile error includes the following steps: Predict the profile error after machining by the prediction model; Determine the input trajectory after pre-compensation of the machine tool linear axis and calculate the actual output position; Calculate the profile error after pre-compensation, and after N iterations, when the maximum profile error value is less than the target allowable maximum profile error, determine the iterative pre-compensation value.

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