An ultrasonic elliptical vibration cutting control method and system

Abstract

This invention relates to the field of precision manufacturing technology and discloses a method and system for controlling ultrasonic elliptical vibration cutting trajectories. The method includes the following steps: S1: Calculating the initial elliptical vibration trajectory equation based on the given cutting profile and tool parameters; S2: Calculating the reference cutting force sequence [f1, f2, f3, ..., f] based on the material parameters being cut, the elliptical vibration trajectory equation, tool parameters, and the cutting layer thickness. Nf ] i S3: Collect the actual cutting force sequence [F1, F2, F3, ..., F] within the current period T, at equal intervals with the reference cutting sequence. Nf ] i S4: Calculate the difference E between the actual cutting force sequence and the reference cutting force sequence for the current cycle. i S5: Through closed-loop control algorithm, based on the difference E i Calculate the rate of change Δk of the cutting slope during periodic vibration; S6: Correct the elliptical vibration trajectory equation based on the rate of change Δk, and control the tool to perform cutting in the next cycle based on the corrected elliptical vibration trajectory equation. This method eliminates the need for tedious leveling or cutting of the workpiece surface, allowing direct ultrasonic elliptical vibration cutting.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of precision manufacturing technology, and particularly relates to an ultrasonic elliptical vibration cutting control method and system. BACKGROUND

[0002] The ultrasonic elliptical vibration cutting is an auxiliary microstructure cutting method which utilizes the machine tool feeding and the periodic ultrasonic elliptical vibration cutting of the tool. When the workpiece surface is uneven, overcutting or undercutting phenomenon is prone to occur during the machining using the traditional ultrasonic elliptical vibration trajectory equation, which greatly affects the quality of the microstructure of the machined surface.

[0003] To solve the above problems, the existing technology is to perform cutting and flattening processing on the workpiece surface, and then perform elliptical trajectory vibration machining. However, this method cannot completely guarantee the flatness of the workpiece installation, and the straightness error of the machine tool guide rail will also cause the elliptical vibration center to jump during the cutting process. The unevenness and inclination of the workpiece surface and the machine tool feeding direction during the cutting process will change the cutting depth during the elliptical vibration cutting process and affect the change of the cutting force. Excessive cutting force is prone to cause cracks in brittle materials during the cutting process, and excessive cutting force will also affect the service life of the tool. Therefore, a cutting control method which can avoid excessive or insufficient cutting force, control the cutting process and make the cutting morphology more accurate is needed to realize ultrasonic elliptical vibration cutting machining on the workpiece surface which is not adjusted or not flattened. SUMMARY

[0004] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide an ultrasonic elliptical vibration cutting control method which can avoid excessive or insufficient cutting force, control the cutting process and make the cutting morphology more accurate, so as to realize ultrasonic elliptical vibration cutting machining on the workpiece surface which is not adjusted or not flattened.

[0005] To solve the above problems, the technical solution adopted by the present application is as follows: an ultrasonic elliptical vibration cutting trajectory control method, comprising the following steps:

[0006] S1: calculating an initial elliptical vibration trajectory equation according to the given cutting morphology and tool parameters;

[0007] S2: calculating a reference cutting force sequence according to the parameters of the machined material, the elliptical vibration trajectory equation, the tool parameters and the cutting layer thickness

[0008] S3: collecting the actual cutting force sequence at equal intervals in the current period T i and the reference cutting sequence

[0009] S4: calculating the current period T iThe difference E between the actual cutting force sequence and the reference cutting force sequence within the range. i ;

[0010] S5: Through closed-loop control algorithm, based on the difference E i Calculate the rate of change Δk of the cutting slope during periodic vibration;

[0011] S6: Correct the elliptical vibration trajectory equation according to the rate of change Δk, and control the tool to perform cutting in the next cycle according to the corrected elliptical vibration trajectory equation.

[0012] Compared to existing technologies, the advantages of this invention are as follows: Since the change in cutting force of the tool during the cutting process can reflect the change in the actual cutting thickness, the actual cutting force sequence of the tool can be collected as feedback, and the difference between it and the ideal cutting force sequence can be calculated. This difference reflects the deviation between the actual cutting trajectory and the ideal cutting trajectory. This method can correct the actual cutting trajectory by calculating this deviation and using a closed-loop control algorithm to correct the vibration trajectory equation. This improves the cutting accuracy of unadjusted or uneven workpieces, avoids excessive cutting force causing workpiece cracks, and increases tool life. It eliminates the need for cumbersome leveling or cutting flattening of the workpiece surface, allowing direct ultrasonic elliptical vibration cutting, thus simplifying the pre-cutting processing steps.

[0013] In the above-described method for controlling the ultrasonic elliptical vibration cutting trajectory, the initial elliptical vibration trajectory equation in step S1 is as follows:

[0014]

[0015] In the formula, F v denoted as the feed rate of the tool along the x-axis, a0 as the amplitude of the initial elliptical vibration trajectory equation in the feed direction, b0 as the amplitude of the initial elliptical vibration trajectory equation in the depth of cut direction, f as the vibration frequency of the initial elliptical vibration trajectory equation, and t as the cutting time.

[0016] In the above-described method for controlling the ultrasonic elliptical vibration cutting trajectory, in step S4, the difference... Where wi,j is the difference weight coefficient of the j-th point in the i-th period.

[0017] In the above-described control method for ultrasonic elliptical vibration cutting trajectory, the closed-loop control algorithm in step S5 is a PID algorithm.

[0018] In the above-described method for controlling the ultrasonic elliptical vibration cutting trajectory, the corrected elliptical vibration trajectory equation in step S6 is shown below:

[0019]

[0020] in

[0021] k i =k i-1 +Δk, k i Let a be the cutting slope of the periodic vibration in the i-th period. ci Let b be the amplitude of the elliptical vibration trajectory equation of the i-th period in the feed direction. ci Let be the amplitude of the elliptical vibration trajectory equation of the i-th period in the tangential direction.

[0022] In the above-described method for controlling the ultrasonic elliptical vibration cutting trajectory, the corrected elliptical vibration trajectory equation in step S6 is shown below:

[0023]

[0024] in,

[0025] k i =k i-1 +Δk,a ci Let b be the amplitude of the elliptical vibration trajectory equation of the i-th period in the feed direction. ci Let be the amplitude of the elliptical vibration trajectory equation of the i-th period in the tangential direction.

[0026] In the above-described method for controlling ultrasonic elliptical vibration cutting trajectory, the elliptical vibration trajectory equation in step S2 is either the initial elliptical vibration trajectory equation or the elliptical vibration trajectory equation of the previous cycle.

[0027] An ultrasonic elliptical vibration cutting system includes a machine tool, a cutting tool, a displacement actuator, a displacement sensor, a cutting force sensor, and a controller. The cutting tool is used to cut a workpiece, the machine tool is used to feed the workpiece, the displacement actuator is used to drive the cutting tool to move, the displacement sensor is used to detect the displacement distance of the cutting tool, and the cutting force sensor is used to detect the actual cutting force of the cutting tool. The machine tool, the displacement actuator, the displacement sensor, and the cutting force sensor are all electrically connected to and controlled by the controller.

[0028] The aforementioned ultrasonic elliptical vibration cutting system includes a controller comprising: an ideal calculation module, used to calculate an initial elliptical vibration trajectory equation based on a given cutting profile and tool parameters, and to calculate a reference cutting force sequence based on the material parameters being cut, the initial elliptical vibration trajectory equation, tool parameters, and cutting layer thickness. The acquisition module is used to control the displacement sensor to acquire the real-time position of the tool, and to control the cutting force sensor to acquire the actual cutting force sequence at equal intervals with the reference cutting sequence. The closed-loop control module is used to calculate the difference E between the actual cutting force sequence and the reference cutting force sequence for the current cycle.i And through a closed-loop control algorithm, based on the difference E i The system calculates the rate of change Δk of the cutting slope during periodic vibration; a correction module is used to correct the elliptical vibration trajectory equation based on the rate of change Δk to obtain the corrected elliptical vibration trajectory equation; and a trajectory tracking module is used to control the displacement actuator to correct the elliptical vibration trajectory equation.

[0029] The aforementioned ultrasonic elliptical vibration cutting system also includes an amplifier, and the displacement actuator is electrically connected to the controller through the amplifier.

[0030] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0031] Figure 1 This is a control principle diagram of the cutting method according to an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of the trajectory for elliptical vibration cutting of an inclined workpiece surface;

[0033] Figure 3 This is a schematic diagram of the cutting trajectory after amplitude correction in the depth of cut direction;

[0034] Figure 4 This is a schematic diagram of the cutting trajectory after amplitude correction in the depth of cut and feed directions.

[0035] Figure 5 This is a simulation displacement result diagram of the cutting method of the present invention used for cutting uneven surfaces according to an embodiment of the invention;

[0036] Figure 6 The cutting method of this invention is used to cut the morphology and morphology error results of an uneven surface.

[0037] Figure 7 This is a block diagram of the control system of the ultrasonic elliptical vibration cutting system according to an embodiment of the present invention. Detailed Implementation

[0038] Example 1:

[0039] Reference Figure 1 The method for controlling the ultrasonic elliptical vibration cutting trajectory according to Embodiment 1 of the present invention includes the following steps:

[0040] S1: Calculate the initial elliptical vibration trajectory equation based on the given cutting shape and tool parameters;

[0041] S2: Calculate the reference cutting force sequence based on the parameters of the material being cut, the equation of the elliptical vibration trajectory, the tool parameters, and the thickness of the cutting layer.

[0042] S3: Collect data for the current period T i The actual cutting force sequence is equidistant from the reference cutting sequence.

[0043] S4: Calculate the current period T i The difference E between the actual cutting force sequence and the reference cutting force sequence within the range. i ;

[0044] S5: Through closed-loop control algorithm, based on the difference E i Calculate the rate of change Δk of the cutting slope during periodic vibration;

[0045] S6: Correct the elliptical vibration trajectory equation according to the rate of change Δk, and control the tool to perform cutting in the next cycle according to the corrected elliptical vibration trajectory equation.

[0046] In step S1, the initial elliptical vibration trajectory equation is calculated based on the given cutting profile and tool parameters, including the feed rate and vibration frequency of the computer tool, as well as the amplitude of the elliptical vibration trajectory equation of the tool in the feed direction and the amplitude in the depth of cut direction, as shown in the following formula:

[0047]

[0048] Among them, F v Let a0 be the feed rate along the x-axis of the tool, b0 be the amplitude of the initial elliptical vibration trajectory equation in the feed direction, f be the vibration frequency of the initial elliptical vibration trajectory equation, and t be the cutting time. The initial elliptical vibration trajectory equation represents the cutting trajectory of the tool under ideal conditions. It should be noted that the tool parameters are common parameters in ultrasonic elliptical vibration cutting, such as the rake angle and cutting edge angle, which can be selected according to the actual situation. The parameters of the material being cut include Young's modulus, etc. The tool parameters and the parameters of the material being cut are not the focus of this application. The focus of step S2 is to obtain the reference cutting force sequence based on these required or provided parameters.

[0049] Based on the above elliptical vibration cutting trajectory, when the workpiece surface to be machined is not parallel to the machine tool feed direction, or when the workpiece surface flatness is poor, overcutting and undercutting defects are prone to occur. Figure 2 As shown. The ultrasonic elliptical vibration trajectory equation cutting method of Embodiment 1 of the present invention can acquire cutting force data of the tool in real time using a non-resonant tool with cutting force sensing function, compare it with the reference cutting force under ideal conditions, obtain the cutting force changes in each cycle, and obtain the tilt angle of the workpiece surface relative to the machine tool feed axis through closed-loop control based on the changes in cutting force. When the cutting force at each point of the cutting trajectory... relatively The smaller value indicates undercutting; the set trajectory slope is less than the workpiece surface inclination slope. Figure 1 As shown, conversely, overcutting occurs. This is achieved by adjusting the difference in cutting force E... i As input to the closed-loop control algorithm, a compensation value with the opposite direction to the deviation can be output to compensate for the topographic error, making the cutting topographic shape basically consistent with the target topographic shape and gradually stabilizing. Using the above cutting method, uneven workpiece surfaces can be directly cut by ultrasonic elliptical vibration without the need for cumbersome leveling or cutting.

[0050] In Example 1, refer to Figure 2 Actual cutting force sequence Spacing and reference cutting force sequence Equal spacing means that the sampling intervals of each cutting force in two sequences are equal in the feed direction of the machine tool. Difference E i The weighted sum of the corresponding deviations between the actual cutting force and the reference cutting force is obtained by the following formula:

[0051]

[0052] F i，j and f i，j These are the actual cutting force sequences in the i-th period. The j-th cutting force value and the reference cutting force sequence in the i-th cycle. The j-th cutting force value in the sequence, where wi,j is the difference weight coefficient sequence of the i-th cycle. The j-th difference weight in w. i，j >0 is used to adjust the weight of the cutting force at each point within a single cycle during the control process. The purpose of summing the weighting coefficients is twofold: first, to ensure the final control deviation includes more effective cutting force deviation information; and second, to amplify the influence of cutting force deviations at effective cutting positions using the weighting coefficients. Generally, the larger the depth of cut, the higher the weighting coefficient. i，j The larger the setting value, the greater the w at the uncut trajectory position. i，j It can be set to zero.

[0053] In Example 1, the closed-loop control algorithm in step S5 adopts the PID algorithm, that is... Right now:

[0054]

[0055] Where k iLet be the slope of the vibration cutting tilt in the i-th cycle. Based on the compensated workpiece surface tilt slope, calculate the amplitude of the corrected elliptical vibration cutting trajectory in the feed direction and depth of cut direction, and obtain the relationship between the corrected elliptical vibration cutting trajectory and the compensated tilt slope.

[0056] Among them, the amplitude b in the corrected depth of cut direction ci It can be obtained from the following formula:

[0057]

[0058] The trajectory equation of the elliptical vibration cutting trajectory at this time is shown in the following formula:

[0059]

[0060] Depend on Figure 3 It can be seen that, after the depth-of-cut correction, although the deepest cutting points of curves P2 and P1 coincide, there is still an undercut region in the elliptical cutting portion. To compensate for this defect, the amplitude 'a' of the elliptical vibration cutting trajectory in the feed direction can be corrected. ci This ensures that the curvature circle R1 at the bottom of the trajectory coincides with the curvature circle R0 of the target trajectory. The revised elliptical trajectory expression is as follows:

[0061]

[0062] To calculate the amplitude 'a' of the corrected elliptical vibration cutting trajectory in the feed direction. ci Give the expression for the radius of curvature of the elliptical trajectory:

[0063]

[0064] And the expression for the radius of curvature at the bottom of the elliptical vibration cutting trajectory:

[0065]

[0066] Reference Figure 4 To ensure that the bottom curvature of the changed elliptical vibration cutting trajectory remains unchanged, even if the bottom curvature radius is the same before and after the trajectory change, we can obtain:

[0067]

[0068] Solving the above equations yields the amplitude of the corrected elliptical vibration cutting trajectory in the feed direction:

[0069]

[0070] The final corrected elliptical vibration cutting trajectory is as follows:

[0071]

[0072] in

[0073] By controlling the tool position through the corrected elliptical vibration cutting trajectory, shape error compensation can be achieved.

[0074] Example 2:

[0075] The difference between Embodiment 2 and Embodiment 1 of the present invention lies in the method for correcting the elliptical vibration cutting trajectory. In Embodiment 1, the correction is based on the amplitudes a0 and b0 of the initial elliptical vibration cutting trajectory, while also referencing the cutting force sequence. It is also a fixed value calculated based on the initial elliptical vibration cutting trajectory. In practice, each correction can be based on the cutting trajectory corrected in the previous cycle, and the reference cutting force sequence can be recalculated based on the corrected trajectory after each correction. As a reference for the next cycle of adjustments.

[0076] In Example 2, the equation for the modified elliptical vibration cutting trajectory is shown below:

[0077]

[0078] in,

[0079] Example 3:

[0080] Embodiment 3 of the present invention provides a specific cutting embodiment: MATLAB is used, and the cutting method of Embodiment 1 of the present invention is employed to simulate ultrasonic elliptical vibration cutting of a micro-pit array. The spacing of the micro-pit array is set to 6.67 μm, and the depth to 1 μm. The workpiece surface is set as a sinusoidal function with gradually increasing amplitude, and the maximum fluctuation during the cutting process is 2.5 μm. The machine tool vibration frequency is set to 300 Hz, the feed rate to 2 mm / s, and the amplitudes of the reference elliptical vibration trajectory equation for the target cutting shape in the depth of cut and feed direction are 4 μm and 1.2 μm, respectively, with a cutting thickness of 1 μm. The simulation duration is 0.5 s, and the cutting length is 1 mm. The initial equation for the elliptical vibration cutting trajectory is:

[0081]

[0082] Based on the parameters of the material being cut, the equation of the elliptical vibration trajectory, the tool parameters, and the thickness of the cutting layer, a preliminary reference cutting force sequence is estimated:

[0083]

[0084] Since the simulation is under ideal conditions, referencing the actual estimated value of the cutting force does not affect the control effect. The number of sequences is N. f =11.

[0085] Weight sequence of the difference:

[0086]

[0087] The control process of elliptical vibration cutting trajectory on an uneven surface is implemented through MATLAB programming. The programming algorithm realizes the discretization of cutting force, weighted summation, PID control process, correction of elliptical vibration cutting trajectory, and generation of the corrected elliptical vibration cutting trajectory. Since the tool physical system is a controlled system, MATLAB simulation is used to realize tool trajectory tracking and the interaction between the tool tip and the workpiece cutting force. The parameter adjustment results of the PID slope error controller are kp = 0.014, ki = 0.0001, kd = 0.001, and the weight sequence is... No adjustments were made during the simulation.

[0088] Simulation results are as follows Figure 5 and Figure 6 As shown, the equation of the elliptical vibration trajectory of the tool tip changes with the unevenness of the workpiece surface, without any defects of undercutting or overcutting. Figure 6 During the cutting process, sub-figures a, b, and c represent the cutting trajectory and target morphology at different stages. It can be seen that the cutting trajectory and target morphology are highly consistent. While the amplitude of the elliptical vibration is corrected in the depth of cut direction, the amplitude in the feed direction also changes, resulting in the cutting thickness and the shape of the micro-pits being basically consistent in sub-figures a, b, and c.

[0089] Figure 6 To assess the morphological error, during the initial cutting stage (0–200 μm), the workpiece surface slowly undulated upwards, exhibiting slight overcutting. The control system quickly corrected the elliptical trajectory, preventing further overcutting. In the 200–500 μm segment, the cut surface gradually moved away from the tool, resulting in undercutting. After correction of the elliptical trajectory by the control system, the undercutting error stabilized at a minimal value. Subsequent rises and falls of the workpiece surface did not result in significant overcutting or undercutting errors. The morphological error stabilized between +0.108 μm and -0.142 μm, and the simulated micro-pit array closely matched the designed micro-pit array morphology.

[0090] Example 4

[0091] Reference Figure 7Embodiment 4 of the present invention provides an ultrasonic elliptical vibration cutting system, including a machine tool, a cutting tool, a displacement actuator, a displacement sensor, a cutting force sensor, and a controller. The cutting tool is used to cut the workpiece, the machine tool is used to feed the workpiece, the displacement actuator is used to drive the cutting tool, the displacement sensor is used to detect the displacement distance of the cutting tool, and the cutting force sensor is used to detect the actual cutting force of the cutting tool. The machine tool, displacement actuator, displacement sensor, and cutting force sensor are all electrically connected to and controlled by the controller.

[0092] The controller includes an ideal calculation module, a data acquisition module, a closed-loop control module, a correction module, and a trajectory tracking module. The ideal calculation module calculates the initial elliptical vibration trajectory equation based on the given cutting profile and tool parameters, and calculates the reference cutting force sequence based on the material parameters, the initial elliptical vibration trajectory equation, tool parameters, and cutting layer thickness. The acquisition module is used to control the displacement sensor to acquire the real-time position of the tool, and to control the cutting force sensor to acquire the actual cutting force sequence at equal intervals with the reference cutting sequence. The closed-loop control module is used to calculate the difference E between the actual cutting force sequence and the reference cutting force sequence for the current cycle. i And through a closed-loop control algorithm, based on the difference E i The rate of change Δk of the cutting slope during periodic vibration is calculated; a correction module is used to correct the elliptical vibration trajectory equation based on the rate of change Δk to obtain the corrected elliptical vibration trajectory equation; a trajectory tracking module is used to control the displacement actuator to correct the elliptical vibration trajectory equation. In some embodiments, the ultrasonic elliptical vibration cutting system further includes an amplifier, and the displacement actuator is electrically connected to the controller through the amplifier.

[0093] It should be noted that in the description of this invention, any descriptions of orientation, such as up, down, front, back, left, right, etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings. They are only for the purpose of facilitating the description of this invention and simplifying the description, and do not indicate or imply that the system or element referred to must have a specific orientation, be constructed or operated in a specific orientation, and should not be construed as a limitation of this invention.

[0094] In the description of this invention, "several" means one or more, "more than" means two or more, "greater than," "less than," "exceeding," etc. are understood to exclude the stated number, while "above," "below," "within," etc. are understood to include the stated number. If "first" or "second" is mentioned, it is only for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0095] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0096] The above embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of protection of the present invention. Any non-substantial changes and substitutions made by those skilled in the art based on the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A method for controlling the trajectory of ultrasonic elliptical vibration cutting, characterized in that, Includes the following steps: S1: Based on the given cutting shape and tool parameters, establish the initial equation for the elliptical vibration trajectory; S2: Based on the parameters of the material being cut, the equation of the elliptical vibration trajectory, the tool parameters, and the thickness of the cutting layer, obtain a reference cutting force sequence for i periods. ; S3: Collect data for the current cycle The actual cutting force sequence within the reference cutting force sequence is at equal intervals. ; S4: Calculate the current cycle The difference between the actual cutting force sequence and the reference cutting force sequence within the range ; S5: Through closed-loop control algorithm, based on the difference Calculate the rate of change of the cutting slope during periodic vibration. ; S6: Based on the rate of change The equation of the elliptical vibration trajectory is corrected, and the tool is controlled to perform cutting in the next cycle based on the corrected equation.

2. The method for controlling the ultrasonic elliptical vibration cutting trajectory according to claim 1, characterized in that, In step S1, the initial equation for the elliptical vibration trajectory is as follows: In the formula, Let x be the feed rate of the tool along the x-axis. Let be the amplitude of the initial elliptical vibration trajectory equation in the feed direction. Let f be the amplitude of the initial elliptical vibration trajectory equation in the cutting depth direction, f be the vibration frequency of the initial elliptical vibration trajectory equation, and t be the cutting time.

3. The method for controlling the ultrasonic elliptical vibration cutting trajectory according to claim 1, characterized in that, In step S4, the difference ,in The difference weighting coefficient is the value at point j in the i-th period.

4. The method for controlling the ultrasonic elliptical vibration cutting trajectory according to claim 1, characterized in that, The closed-loop control algorithm in step S5 is the PID algorithm.

5. The method for controlling the ultrasonic elliptical vibration cutting trajectory according to claim 2, characterized in that, In step S6, the corrected equation for the elliptical vibration trajectory is shown below: in, ， , Let be the cutting slope of the periodic vibration in the i-th period. Let be the amplitude of the elliptical vibration trajectory equation of the i-th period in the feed direction. Let be the amplitude of the elliptical vibration trajectory equation of the i-th period in the tangential direction.

6. The method for controlling the ultrasonic elliptical vibration cutting trajectory according to claim 2, characterized in that, In step S6, the corrected equation for the elliptical vibration trajectory is shown below: in, ， , Let be the cutting slope of the periodic vibration in the i-th period. Let be the amplitude of the elliptical vibration trajectory equation of the i-th period in the feed direction. Let be the amplitude of the elliptical vibration trajectory equation of the i-th period in the tangential direction.

7. The method for controlling the ultrasonic elliptical vibration cutting trajectory according to claim 1, characterized in that, The elliptical vibration trajectory equation in step S2 is either the initial elliptical vibration trajectory equation or the elliptical vibration trajectory equation of the previous period.

8. An ultrasonic elliptical vibration cutting system, characterized in that, A control method for implementing the ultrasonic elliptical vibration cutting trajectory as described in any one of claims 1-7 includes a machine tool, a cutting tool, a displacement actuator, a displacement sensor, a cutting force sensor, and a controller. The cutting tool is used to cut a workpiece, the machine tool is used to clamp and feed the workpiece, the displacement actuator is used to drive the cutting tool to move, the displacement sensor is used to detect the displacement of the cutting tool, and the cutting force sensor is used to detect the actual cutting force of the cutting tool. The machine tool, the displacement actuator, the displacement sensor, and the cutting force sensor are all electrically connected to and controlled by the controller.

9. The ultrasonic elliptical vibration cutting system according to claim 8, characterized in that, The controller includes: The ideal calculation module is used to calculate the initial elliptical vibration trajectory equation based on the given cutting profile and tool parameters, and to calculate the reference cutting force sequence based on the material parameters being cut, the initial elliptical vibration trajectory equation, tool parameters, and cutting layer thickness. ; The acquisition module is used to control the displacement sensor to acquire the real-time position of the tool, and to control the cutting force sensor to acquire the actual cutting force sequence at equal intervals with the reference cutting sequence. ; The closed-loop control module is used to calculate the difference between the actual cutting force sequence and the reference cutting force sequence for the current cycle. And through a closed-loop control algorithm, based on the difference Calculate the rate of change of the cutting slope during periodic vibration. ; Correction module, used to adjust according to the rate of change The equation of the elliptical vibration trajectory is modified to obtain the modified equation of the elliptical vibration trajectory. The trajectory tracking module is used to control the displacement actuator to correct the elliptical vibration trajectory according to the modified equation.

10. The ultrasonic elliptical vibration cutting system according to claim 9, characterized in that, It also includes an amplifier, through which the displacement actuator is electrically connected to the controller.

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