Multi-frequency elliptical vibration auxiliary cutting method and system

Abstract

The invention belongs to the related field of ultrasonic elliptical vibration turning technology, and discloses a multi-frequency elliptical vibration auxiliary cutting method, which comprises the following steps of: acquiring a corresponding curved surface trajectory equation f (t) for a curved surface to be processed; when the curved surface trajectory equation f (t) meets the Dirichlet condition, the curved surface trajectory equation f (t) is gradually expanded in the form of a Fourier series trigonometric function expansion Ln (t), and the error between the trigonometric function and the curved surface trajectory equation is calculated and judged after each expansion until the two equations meet the fitting requirement; and superposing the cutting track expression fe (t) to the trigonometric function in the final expansion so as to obtain a final cutting processing track, and correspondingly executing cutting processing. The invention further discloses a corresponding system. By means of the method, turning machining of complex curved surfaces of various materials difficult to machine can be more efficiently and conveniently achieved, low-frequency vibration can be used for generating a free-form surface contour, and high-frequency ultrasonic vibration is used for improving the machinability in the material removing process.

Description

Technical Field

[0001] The present invention belongs to the field related to ultrasonic elliptical vibration turning technology, and more specifically, relates to a multi-frequency elliptical vibration assisted cutting method and system. Background Art

[0002] Ultrasonic elliptical vibration turning technology is widely used in existing processing methods. For example, in the processing of difficult-to-process materials and ultra-precision processing, this cutting technology not only solves traditional processing problems, but also demonstrates many unique advantages: reducing cutting force, inhibiting tool wear, reducing surface roughness, etc. Therefore, it is widely used in the processing of various difficult-to-process materials in the fields of national defense, military, biomedicine, etc.

[0003] Currently, ultrasonic vibration-assisted machining of free-form surfaces mostly uses machine tool CNC codes to generate tool path planning. However, this method is complex and has error risks during the writing process, requires a lot of time for debugging and optimization, and has high requirements on the skills of the operator.

[0004] Accordingly, this field urgently needs further research and improvement in order to better meet the needs of creating free-form surfaces of difficult-to-machine materials. Summary of the invention

[0005] In response to one or more of the above-mentioned defects or needs of the prior art, the present invention provides a multi-frequency elliptical vibration assisted cutting method and system, which fully combines the characteristics and requirements of ultrasonic elliptical vibration cutting processing, introduces the Fourier series trigonometric function expansion to fit the processing trajectory and makes targeted improvements to the specific fitting process, which can correspondingly realize the turning processing of complex surfaces of various difficult-to-process materials more efficiently and conveniently.

[0006] To achieve the above object, according to a first aspect of the present invention, a multi-frequency elliptical vibration assisted cutting method is provided, characterized in that the method comprises the following steps:

[0007] S1. Obtain the corresponding surface trajectory equation f(t) for the surface to be processed;

[0008] S2. When the surface trajectory equation f(t) satisfies the Dirichlet condition, the following Fourier series trigonometric function expansion L is used for it: n (t) is expanded in the form of:

[0009]

[0010] Among them, a0 is a constant term; a n is the coefficient of the even function term, b n are the odd function coefficients, representing the frequency component and amplitude of the trigonometric function within the period; ω ois the angular frequency; n represents the number of expansions;

[0011] S3, let n=1;

[0012] S4, the surface trajectory equation f(t) at this time, the Fourier series trigonometric function expansion L n (t) Perform equidistance discretization on the initial definition domain (0, t0], and then use the least squares method to calculate the error μ between the two;

[0013] S5. Determine the magnitude relationship between the calculated error μ and the minimum value ε in combination with the preset minimum value ε: if μ>ε, return to step S3 and set n=n+1; if μ≤ε, directly proceed to step S6;

[0014] S6. The ultrasonic elliptical vibration cutting trajectory expression f e (t) The Fourier series trigonometric function expansion L when superimposed to the final expansion n (t), thereby obtaining the final cutting machining trajectory and performing the cutting machining accordingly.

[0015] As a further preferred embodiment of the present invention, in step S4, the spacing of the equidistant dispersion processing is preferably set to Wherein m represents a natural number greater than or equal to 3.

[0016] As a further preferred embodiment of the present invention, in step S4, the calculation formula for calculating the error μ using the least squares method is preferably expressed as follows:

[0017]

[0018] As a further preferred embodiment of the present invention, in step S6, the ultrasonic elliptical vibration cutting trajectory expression f e (t) The preferred design is as follows:

[0019]

[0020] Among them, a e 、b e are the amplitudes along the x and y directions during ultrasonic elliptical vibration-assisted cutting, ω h is the angular frequency during ultrasonic vibration-assisted cutting, is the phase difference between the x and y directions.

[0021] As a further preferred embodiment of the present invention, in step S6, the expression of the final cutting trajectory is preferably designed as follows:

[0022]

[0023] Among them, v cis the cutting speed along the x direction, L n (t) is the trigonometric function expansion of the Fourier series at the final expansion.

[0024] As a further preferred embodiment of the present invention, the curved surface to be processed is a complex curved surface made of a difficult-to-process material.

[0025] According to a second aspect of the present invention, a corresponding computer-readable storage medium is provided, characterized in that the computer-readable storage medium stores machine-executable instructions, and the machine-executable instructions implement the above-mentioned multi-frequency elliptical vibration-assisted cutting method.

[0026] According to the third aspect of the present invention, a corresponding multi-frequency elliptical vibration assisted cutting system is also provided, which includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the above-mentioned multi-frequency elliptical vibration assisted cutting method when executing the computer program.

[0027] In general, compared with the prior art, the above technical scheme conceived by the present invention fits the processing trajectory by introducing the Fourier series trigonometric function expansion and makes targeted improvements to the specific fitting process, which can more efficiently and conveniently realize the turning processing of complex surfaces of various difficult-to-process materials; in addition, the present invention can further use low-frequency vibration to generate free-form surface contours, and high-frequency ultrasonic vibration to improve the machinability during material removal, thereby realizing the creation of free-form surfaces of difficult-to-process materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a process flow chart for exemplarily illustrating the multi-frequency elliptical vibration assisted cutting method according to the present invention;

[0029] Figure 2 A multi-frequency elliptical vibration assisted cutting system for exemplifying the multi-frequency elliptical vibration assisted cutting method of the present invention;

[0030] Figure 3 It is a longitudinal-bending composite vibration two-dimensional ultrasonic elliptical vibration cutting device in a multi-frequency elliptical vibration assisted cutting device;

[0031] Figure 4 It is a comparison diagram for displaying the initial tool path and the first-order fitted Fourier series trigonometric function path according to a specific example;

[0032] Figure 5 It is a comparison diagram for displaying the initial tool path and the fourth-order fitting Fourier series trigonometric function path according to a specific example;

[0033] Figure 6It is a comparison diagram for displaying the initial tool path and the seventh-order fitted Fourier series trigonometric function path according to a specific example;

[0034] Figure 7 It is a composite processing trajectory diagram obtained according to a specific example.

[0035] Throughout the drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0036] 1- non-resonant vibration cutting device; 2- stacked piezoelectric ceramics; 3- power amplifier; 4- signal generator; 5- longitudinal-bending composite two-dimensional ultrasonic elliptical vibration cutting device; 501- bolt; 502- electrode sheet; 503- longitudinal vibration piezoelectric ceramic full circle ring; 504- bending vibration piezoelectric ceramic semicircular ring; 505- front cover plate; 506- middle cover plate; 507- rear cover plate; 508- amplitude transformer; 6- housing; 7- tool. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0038] Figure 1 is a process flow chart for exemplifying the multi-frequency elliptical vibration assisted cutting method according to the present invention, and will be referred to below. Figure 1 To explain the present invention in more detail.

[0039] The first step is to obtain the corresponding surface trajectory equation f(t) for the surface to be processed.

[0040] In the second step, when the surface trajectory equation f(t) satisfies the Dirichlet condition, the following Fourier series trigonometric function expansion L is used for it: n (t) is expanded in the form of:

[0041]

[0042] Among them, a0 is a constant term; a n is the coefficient of the even function term, b n are the coefficients of odd functions, representing the frequency components and amplitudes of trigonometric functions within the period; ω0 is the angular frequency; and n represents the number of expansions.

[0043] More specifically, as is common knowledge in the art, the Dirichlet condition can be expressed as follows:

[0044] a. The function is absolutely integrable in any period;

[0045] b. The function has only a finite number of extreme points in any period;

[0046] c. There are only a finite number of first-kind discontinuity points in any period of the function.

[0047] The third step is to set n=1 and start the first expansion.

[0048] The fourth step is to convert the surface trajectory equation f(t) and the Fourier series trigonometric function expansion L n (t) is discretized on the initial domain (0, t0] with equal distances, and then the error μ between the two is calculated using the least squares method.

[0049] More specifically, according to a preferred embodiment of the present invention, the spacing of the equidistant dispersion process is preferably set to Wherein m represents a natural number greater than or equal to 3. In addition, the calculation formula for calculating the error μ using the least squares method can preferably be expressed as follows:

[0050]

[0051] Step 5: Combined with the preset minimum value ε, determine the size relationship between the calculated error μ and the minimum value ε: if μ>ε, return to step S3 and set n=n+1; if μ≤ε, directly proceed to the next step;

[0052] Step 6: Transform the ultrasonic elliptical vibration cutting trajectory expression f e (t) The Fourier series trigonometric function expansion L when superimposed to the final expansion n (t), thereby obtaining the final cutting machining trajectory and performing the cutting machining accordingly.

[0053] More specifically, according to a preferred embodiment of the present invention, the ultrasonic elliptical vibration cutting trajectory expression f e (t) The preferred design is as follows:

[0054]

[0055] Among them, a e 、b e are the amplitudes along the x and y directions during ultrasonic elliptical vibration-assisted cutting, ω h is the angular frequency during ultrasonic vibration-assisted cutting, is the phase difference between the x and y directions.

[0056] Accordingly, the expression of the final cutting trajectory can preferably be expressed as follows:

[0057]

[0058] Among them, v c is the cutting speed along the x direction, L n (t) is the trigonometric function expansion of the Fourier series at the final expansion.

[0059] Figure 2 It is used to exemplarily illustrate the multi-frequency elliptical vibration assisted cutting system according to the present invention, including a non-resonant vibration cutting device 1, a stacked piezoelectric ceramic 2, a power amplifier 3, a signal generator 4, a longitudinal-bending composite two-dimensional ultrasonic elliptical vibration cutting device 5, a housing 6 and a tool 7. The non-resonant vibration cutting device 1 is installed on the slide of the machine tool through a threaded hole during the processing, the stacked piezoelectric ceramic 2 is installed in the mounting groove of the non-resonant vibration cutting device 1, the longitudinal-bending composite two-dimensional ultrasonic elliptical vibration cutting device 5 is fixedly installed in the housing 6, the housing 6 is fixedly installed on the non-resonant vibration cutting device 1 by screws, and the tool is fixedly installed in the tool mounting hole in the longitudinal-bending composite two-dimensional ultrasonic elliptical vibration cutting device.

[0060] During use, signal generator 1 in the signal generator inputs a low-frequency vibration signal according to the free-form surface machining trajectory, and signal generator 2 inputs a high-frequency ultrasonic signal according to the machining requirements. After the two signals are amplified by the static power amplifier, they are respectively input into the stacked piezoelectric ceramic 2, the longitudinal vibration piezoelectric ceramic full circle ring 503 and the bending vibration piezoelectric ceramic semicircle ring 504 in the longitudinal-bending composite two-dimensional ultrasonic elliptical vibration cutting device. By adjusting the amplitude, frequency and phase difference of the low-frequency and high-frequency signals, the composite trajectory at the tool tip in the multi-frequency elliptical vibration assisted cutting device can be controlled to meet the requirements for efficient and high-precision manufacturing of the target surface.

[0061] like Figure 3As shown, the longitudinal-bending composite two-dimensional ultrasonic elliptical vibration cutting device 5 is used to generate a high-frequency elliptical vibration trajectory at the tip of the tool, including a bolt 501, six electrode sheets 502, two longitudinal vibration piezoelectric ceramic full-circle rings 503, four bending vibration piezoelectric ceramic semi-circle rings 504, a front cover plate 505, a middle cover plate 506, a rear cover plate 507 and an amplitude transformer 508, wherein every two bending vibration piezoelectric ceramic semi-circle rings 504 form a bending vibration piezoelectric ceramic group. The bolt 501 passes through the threaded hole on the front cover plate 505, passes through the electrode sheet 502 and the two longitudinal vibration piezoelectric ceramic full-circle rings 503, the middle cover plate 506, the bending vibration piezoelectric ceramic group, the rear cover plate 507 and the amplitude transformer 508 in sequence, and completes the connection of the ultrasonic vibration device. The electrode sheet 502 is bonded to the longitudinal vibration piezoelectric ceramic full-circle ring 503 and the two sides of the bending vibration piezoelectric ceramic group by JW-1 epoxy resin glue. When the longitudinal-bending composite two-dimensional ultrasonic elliptical vibration cutting device 5 is started, the ultrasonic generator transmits a high-frequency alternating current signal to two groups of bending vibration piezoelectric ceramic groups consisting of two longitudinal vibration piezoelectric ceramic full circle rings 503 and four bending vibration piezoelectric ceramic semi-circular rings 504. Since the piezoelectric material has a reverse piezoelectric effect, the two longitudinal vibration piezoelectric ceramic full circle rings 503 and the two groups of bending vibration piezoelectric ceramic groups vibrate in the axial and radial directions respectively and generate resonance, thereby synthesizing a longitudinal-bending two-dimensional elliptical ultrasonic vibration at the tip of the tool, and superimposing the trajectory generated by the low-frequency vibration signal to achieve the generation of a composite trajectory.

[0062] The following will be combined Figure 1 , Figure 4-Figure 7 A specific embodiment of the present invention will be explained in more detail.

[0063] Example 1

[0064] First, the curve equation f(t) is obtained according to the processed surface;

[0065] Next, determine whether the curve equation f(x) satisfies the Dirichlet condition. If so, proceed to the following steps;

[0066] For the trajectory equation z=f(t) that satisfies the Dirichlet condition, the Fourier series trigonometric function form is expanded, and the expanded expression L n (t) are as follows:

[0067]

[0068] In the formula, a0 is a constant term, representing the average value of the function within the period; a n is the coefficient of the even function term, b n is the coefficient of the odd function, which represents the frequency component and amplitude of the function within the period; ω0 is the angular frequency.

[0069] Let n = 1, and the obtained first-order Fourier series trigonometric function expansion L1(t) is as follows:

[0070]

[0071] In the formula, a1 and b1 are the coefficients of the even function term and the odd function term respectively when n = 1. According to the initial definition domain (0, t0] of the original curve trajectory equation z = f(t), L1(t) and z = f(t) can be equally spaced, and the partition spacing can be preferably designed as Calculate the curve trajectory equation z = f(t) and the first-order Fourier series trigonometric function expansion L1(t). The values ​​of each point after equal interval division are f(t j )| j＝1，...m and L1(t j )| j＝1，...m .

[0072] Then, according to the least squares method, calculate The value of .

[0073] Next, customize the minimum value ε, and compare the value of μ with the minimum value ε according to the calculated μ. If the value of μ is less than or equal to the minimum value ε, it means that the first-order Fourier series trigonometric function expansion L1(t) has a high degree of fit with the curve trajectory equation and can meet the processing requirements. If the value of μ is greater than the minimum value ε, it means that the first-order Fourier series trigonometric function expansion L1(t) has a poor fit with the curve trajectory equation. Let n = n + 1 and repeat the above operation.

[0074] Finally, the ultrasonic elliptical vibration cutting trajectory expression f e (t) The Fourier series trigonometric function expansion L when superimposed to the final expansion n (t), thereby obtaining the final cutting trajectory, and executing the cutting process accordingly. When the signal generator 4 inputs a signal to the stacked piezoelectric ceramic 2, the frequency component size is maintained in accordance with the Fourier series trigonometric function expansion L n (t) The medium and low frequency vibrations in the final composite trajectory meet L by adjusting the amplitude and phase difference of the input voltage signal. n (t).

[0075] In this embodiment, for example, the tool trajectory equation is set to z=e 2sint , the interval is [0, 2π], the ultrasonic vibration parameters are: a = 40μm, b = 20μm, f = 40kHz, the phase difference between the two directions is 90°, and the tool cutting speed v c =0.01*2πfa.

[0076] like Figure 4As shown in the figure, when the first-order Fourier series trigonometric function expansion is used, the initial tool path equation fits poorly with the first-order Fourier series trigonometric expansion. The initial minimum value ε = 0.005 is set. After calculation, the error between the two curves μ = 20903.825 does not meet the requirements, so further iteration is required.

[0077] like Figure 5 As shown in the figure, when iterating to the fourth order, that is, the fourth-order Fourier series trigonometric function expansion, as shown in the attached Figure 3 As shown. The fourth-order Fourier series trigonometric function expansion and the initial tool trajectory z = e 2sint The overall fit is good, and the error between the two curves is μ=3.967, which is significantly lower than the first-order Fourier series trigonometric function expansion. However, there are large deviations locally and they are still greater than the minimum value ε, so further iteration is still needed.

[0078] like Figure 6 As shown in the figure, when iterating to the 7th order, that is, the 7th order Fourier series trigonometric function expansion, as shown in the attached Figure 6 As shown. Overall, the seventh-order Fourier series trigonometric function expansion is similar to the fourth-order Fourier series trigonometric function expansion, which is similar to the initial tool trajectory z = e 2sint The fitting is good, and the error between the seventh-order Fourier series trigonometric function expansion and the initial tool trajectory is μ=0.0012, which is less than the minimum value ε, indicating that the seventh-order Fourier series trigonometric function expansion can meet the processing requirements. The ultrasonic elliptical vibration parameters can be superimposed on the seventh-order Fourier series trigonometric function expansion, as shown in the attached figure. Figure 7 As shown. The frequencies of each item in the seventh-order Fourier series trigonometric function expansion are low-frequency vibrations compared to the ultrasonic elliptical vibration frequency, and are mainly used to fit the initial tool trajectory, that is, the generation of free-form surface machining trajectory. Ultrasonic vibration-assisted cutting is mainly used to improve the machinability of difficult-to-machine materials due to its advantages of reducing cutting force and suppressing cutting heat during machining. At this time, the composite machining trajectory can be expressed as:

[0079]

[0080] It should be noted that, as some special cases, when the curve trajectory equation is z = Asinω1t, its first-order Fourier series trigonometric function expansion L1(t) = b1sinω1t, at this time, the constant term a0 and the even function term coefficient a1 are both 0, that is, a0 = a1 = 0, and the odd function term coefficient b1 value is the same as the curve trajectory equation amplitude A, that is, b1 = A. In this case, the μ value is 0, and the curve trajectory equation and the first-order Fourier series trigonometric function expansion L1(t) have a 100% fit.

[0081] When the curve trajectory equation is z = Bcosω1t, its first-order Fourier series trigonometric function expansion L1(t) = a1cos ω1t, at this time, the constant term a0 and the odd function term coefficient a1 are both 0, that is, a0 = b1 = 0, and the even function term coefficient a1 value is the same as the curve trajectory equation amplitude B, that is, a1 = B. In this case, the μ value is 0, and the curve trajectory equation and the first-order Fourier series trigonometric function expansion L1(t) are also 100% fit.

[0082] In summary, the multi-frequency elliptical vibration assisted cutting method according to the present invention can more efficiently and conveniently realize the turning processing of complex surfaces of various difficult-to-process materials; in addition, the present invention can also use low-frequency vibration for the generation of free-form surface contours, and high-frequency ultrasonic vibration for improving the machinability during material removal, thereby realizing the creation of free-form surfaces of difficult-to-process materials, and thus has good practical value and application prospects.

[0083] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-frequency elliptical vibration assisted cutting method, characterized in that: The method comprises the following steps: S1. Obtain the corresponding surface trajectory equation f(t) for the surface to be processed; S2. When the surface trajectory equation f(t) satisfies the Dirichlet condition, the following Fourier series trigonometric function expansion L is used for it: n (t) is expanded in the form of: Among them, a0 is a constant term; a n is the coefficient of the even function term, b n are the coefficients of odd functions, representing the frequency components and amplitudes of trigonometric functions in the period; ω0 is the angular frequency; n represents the number of expansions; S3, let n=1; S4, the surface trajectory equation f(t) at this time, the Fourier series trigonometric function expansion L n (t) Perform equidistance discretization on the initial definition domain (0, t0], and then use the least squares method to calculate the error μ between the two; S5. Determine the magnitude relationship between the calculated error μ and the minimum value ε in combination with the preset minimum value ε: if μ>ε, return to step S3 and set n=n+1; if μ≤ε, directly proceed to step S6; S6. The ultrasonic elliptical vibration cutting trajectory expression f e (t) The Fourier series trigonometric function expansion L when superimposed to the final expansion n (t), thereby obtaining the final cutting machining trajectory and performing the cutting machining accordingly.

2. The multi-frequency elliptical vibration assisted cutting method according to claim 1, characterized in that: In step S4, the spacing of the equidistant binning process is preferably set to Wherein m represents a natural number greater than or equal to 3.

3. The multi-frequency elliptical vibration assisted cutting method according to claim 2, characterized in that: In step S4, the calculation formula for calculating the error μ using the least squares method is preferably expressed as follows:

4. The multi-frequency elliptical vibration assisted cutting method according to any one of claims 1 to 3, characterized in that: In step S6, the ultrasonic elliptical vibration cutting trajectory expression f e (t) The preferred design is as follows: Among them, a e 、b e are the amplitudes along the x and y directions during ultrasonic elliptical vibration-assisted cutting, ω h is the angular frequency during ultrasonic vibration-assisted cutting, is the phase difference between the x and y directions.

5. The multi-frequency elliptical vibration assisted cutting method according to claim 4, characterized in that: In step S6, the expression of the final cutting trajectory is preferably designed as follows: Among them, v c is the cutting speed along the x direction, L n (t) is the trigonometric function expansion of the Fourier series at the final expansion.

6. The method according to any one of claims 1 to 5, wherein: The curved surface to be processed is a complex curved surface made of difficult-to-process materials.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, and the machine-executable instructions implement the multi-frequency elliptical vibration-assisted cutting method described in any one of claims 1-6.

8. A multi-frequency elliptical vibration assisted cutting system, the system comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the multi-frequency elliptical vibration assisted cutting method described in any one of claims 1 to 6 when executing the computer program.

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