Resonant and non-resonant integrated double-frequency vibration modulation cutting device and cutting method thereof

By using resonant and non-resonant integrated dual-frequency vibration modulation cutting device on difficult-to-process materials, combining low-frequency and high-frequency vibration, the problem of difficult-to-process optical free surface is solved, and high-precision processing effect is achieved.

CN119526028APending Publication Date: 2025-02-28NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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Patent Information

Application Number
CN202411658972.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-20
Publication Date
2025-02-28

AI Technical Summary

Technical Problem

The prior art has difficulty in machining optical free surfaces with high precision on difficult-to-process materials, especially in creating free surfaces and micro-nano structure functional surfaces.

Method used

The resonant and non-resonant integrated dual-frequency vibration modulation and cutting device is adopted to generate low-frequency and large-amplitude vibration vibrations through the non-resonant vibration device, and combined with the high-frequency ultrasonic elliptical vibration generated by the two-dimensional ultrasonic vibration device, the dual-frequency vibration modulation of the tool relative to the workpiece is realized, forming a two-dimensional elliptical vibration trajectory to improve processing accuracy.

Benefits of technology

It realizes high-precision processing of optical free surfaces on difficult-to-machined materials, improves machinability during material removal, reduces tool wear, extends tool service life, and improves machining efficiency and quality.

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Abstract

The invention discloses a resonant and non-resonant integrated double-frequency vibration modulation cutting device and a cutting method.The device comprises a non-resonant vibration device and a two-dimensional ultrasonic vibration device, and the non-resonant vibration device comprises a frame, a flexible hinge mechanism and a piezoelectric ceramic stack; the flexible hinge mechanism transmits the displacement applied by the piezoelectric ceramic stack in the Z-axis direction to the two-dimensional ultrasonic vibration device; the two-dimensional ultrasonic vibration device comprises an ultrasonic amplitude-change pole, a cutter is mounted at the front end of the ultrasonic amplitude-change pole, and an ultrasonic transducer is mounted at the rear end of the ultrasonic amplitude-change The flexible hinge mechanism, the frame and a rear cover plate of the ultrasonic transducer are of an integrated structure. Low-frequency and large-amplitude vibration generated by the non-resonant vibration device is used as a quick tool servo function, a free-form surface contour is generated through low-frequency reciprocating motion, and the machinability in the material removal process is improved through ultrasonic elliptical vibration generated by the two-dimensional ultrasonic vibration device. And furthermore, the optical free-form surface can be processed on a difficult-to-process material with high precision.
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Description

Technical Field

[0001] The invention relates to ultra-precision machining equipment, and in particular to an integrated dual-frequency vibration modulation cutting device based on a resonant and non-resonant combined working mode and a cutting method thereof. Background Art

[0002] Optical free-form surfaces are optical surfaces with arbitrarily complex shapes, which can greatly enhance the performance of optical systems. Compared with traditional rotationally symmetrical surfaces, free-form surfaces are more difficult to process due to their structural complexity and non-rotational symmetry. In addition, some difficult-to-process materials such as ceramics, glass, cemented carbide, titanium alloy, hardened steel, etc. are usually used to process free-form optical elements or molds. These difficult-to-process materials usually have the characteristics of high hardness, high strength, high brittleness, low thermal conductivity, and active chemical properties, which make the machinability poor. During the cutting process, it is very easy to produce high temperature, tool wear, crack proliferation and expansion, etc., which not only reduces the service life of the tool, but also seriously affects the quality and efficiency of processing.

[0003] In order to efficiently, accurately and cost-effectively create complex optical surfaces and micro-nanostructure functional surfaces of difficult-to-process materials, many scholars have conducted extensive research and proposed processing methods such as photolithography, laser processing, electrospark machining, focused ion beam machining, electron beam machining, and diamond cutting. Diamond turning technology based on fast tool servo has high processing accuracy, surface quality and processing efficiency, so it is widely used in the processing of ultra-precision complex structures and free-form surfaces. However, when cutting difficult-to-process materials, fast tool servo diamond turning technology is difficult to achieve free-form surface creation on these materials due to severe tool wear.

[0004] The ultrasonic elliptical vibration cutting method is to superimpose a high-frequency vibration in the traditional main cutting motion direction and the cutting depth direction respectively, to generate an elliptical vibration trajectory, so that the tool and the workpiece are separated periodically. Compared with the traditional cutting method, ultrasonic elliptical vibration cutting has many advantages such as reducing cutting force, inhibiting tool wear, improving processing accuracy and surface quality, reducing chip thickness and facilitating ductile cutting of brittle materials, etc. It has been widely used in the cutting of various difficult-to-process materials. Although ultrasonic elliptical vibration cutting can achieve high-quality processing of some difficult-to-process materials, it is difficult to directly create free-form surfaces by ultrasonic elliptical vibration cutting. The depth of the free-form surface is limited by the amplitude. The depth of the free-form surface is usually between a few microns and hundreds of microns, while the amplitude of the elliptical vibration is usually a few microns.

[0005] Vibration devices are divided into resonant vibration devices and non-resonant vibration devices according to their working principles. Vibration devices based on the resonance principle have a high operating frequency, but a small vibration amplitude and a fixed operating frequency. They are often used to improve the cutting performance of difficult-to-process materials. Compared with resonant vibration devices, non-resonant vibration devices have a lower operating frequency, but the vibration parameters of the device can be set and adjusted arbitrarily, and the device can also be easily controlled to achieve simultaneous output of vibrations of multiple frequency components. Therefore, they are often used in the processing of complex microstructures. It can be seen that vibration devices with a single working mode are difficult to meet the needs of creating free-form surfaces of difficult-to-process materials. Summary of the invention

[0006] Purpose of the invention: The purpose of the present invention is to provide a resonant and non-resonant integrated dual-frequency vibration modulation cutting device and a cutting method thereof in order to address the problem that a vibration device with a single working mode is unable to meet the requirements of free-form surface creation of difficult-to-process materials.

[0007] Technical solution: The resonant and non-resonant integrated dual-frequency vibration modulation cutting device described in the present invention has a front-to-back symmetrical structure as a whole, including a non-resonant vibration device and a two-dimensional ultrasonic vibration device;

[0008] The non-resonant vibration device includes a flexible hinge mechanism, a piezoelectric ceramic stack, a frame and a Z-axis direction pre-tightening screw, the frame is U-shaped, and the opening faces left; the flexible hinge mechanism is U-shaped, and the two ends of the flexible hinge mechanism are connected to the inner wall of the frame, and the opening also faces left; the piezoelectric ceramic stack is located between the flexible hinge mechanism and the frame, and the Z-axis direction pre-tightening screw passes through the frame from the right side and is connected to the threaded connection end of the piezoelectric ceramic stack;

[0009] The two-dimensional ultrasonic vibration device includes an ultrasonic amplitude transformer arranged along the Z-axis direction, a tool is installed at the front end of the ultrasonic amplitude transformer, and an ultrasonic transducer is installed at the rear end; the rear cover plate of the ultrasonic transducer is connected to the inner wall of the flexible hinge mechanism through a flange support structure; the flexible hinge mechanism, the frame and the rear cover plate are an integrated structure; the piezoelectric ceramic stack is used to apply displacement in the Z-axis direction to the flexible hinge mechanism, and the flexible hinge mechanism is used to output the displacement in the Z-axis direction to the two-dimensional ultrasonic vibration device.

[0010] Furthermore, the ultrasonic transducer adopts a square cross-section structure, including a bending vibration type piezoelectric ceramic group and a longitudinal vibration type piezoelectric ceramic. The bending vibration type piezoelectric ceramic group is used to generate bending vibration in the Y-axis direction, and the longitudinal vibration type piezoelectric ceramic is used to generate longitudinal vibration in the Z-axis direction.

[0011] The two-dimensional ultrasonic vibration device (resonant vibration device) of the present invention adopts a square cross-section transducer design. Compared with the traditional circular cross-section transducer, it can better control the direction of bending vibration (Y-axis direction) so as to fit the longitudinal vibration along the Z-axis direction to generate an elliptical vibration trajectory, reduce the parasitic motion that may be generated in the X-axis direction, and improve the machinability during the removal of difficult-to-machine materials. The two-dimensional ultrasonic vibration device generates vibrations in two directions through a longitudinal vibration type piezoelectric ceramic and a bending vibration type piezoelectric ceramic group, and can realize the output of an elliptical trajectory. The direction of the elliptical trajectory is modulated by inputting longitudinal vibration and bending vibration frequency signals with different phase differences, thereby reducing the influence of installation errors on the machining effect and improving the cutting performance of difficult-to-machine materials.

[0012] Furthermore, the bending vibration type piezoelectric ceramic group is composed of two groups of half-square piezoelectric ceramics, and each group of bending vibration type piezoelectric ceramics is composed of two half-square piezoelectric ceramics with opposite polarization directions.

[0013] Furthermore, the longitudinal vibration type piezoelectric ceramic is composed of two stacked piezoelectric ceramic square sheets.

[0014] Furthermore, the ultrasonic horn and the ultrasonic transducer are fixed by pre-tightening bolts.

[0015] Furthermore, the ultrasonic transducer also includes a front cover plate, and the pre-tightening bolts pass through the rear cover plate, the longitudinal vibration type piezoelectric ceramic, the bending vibration type piezoelectric ceramic group and the front cover plate in sequence, and are finally fixed to the rear end face of the ultrasonic amplitude transformer.

[0016] Furthermore, the frame is provided with bolt holes for connecting to the guide rails of the machine tool.

[0017] Furthermore, the flexible hinge mechanism is integrally connected to the frame via an arc-shaped hinge.

[0018] Furthermore, the left end surfaces of the frame and the flexible hinge mechanism are flush.

[0019] The cutting method of the resonant and non-resonant integrated dual-frequency vibration modulation cutting device described in the present invention is that in the Y-axis and Z-axis directions, the tool is driven by the ultrasonic vibration frequency f1 with a certain phase difference in two directions generated by a two-dimensional ultrasonic vibration device to form a two-dimensional elliptical vibration trajectory, which is used to improve the machinability during material removal; the tool is acted upon by the large-amplitude low-frequency oscillation f2 generated by the non-resonant vibration device in the Z-axis direction to achieve the creation of a free-form surface contour; and dual-frequency vibration modulation of the tool relative to the workpiece is achieved through the coupling of high-frequency ultrasonic elliptical vibration and low-frequency oscillation.

[0020] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0021] (1) The dual-frequency vibration modulation cutting device provided by the present invention combines the processing advantages of ultrasonic elliptical vibration cutting and fast tool servo diamond turning technology, uses a non-resonant vibration device to generate low-frequency, large-amplitude vibration as a function of fast tool servo, generates a free-form surface contour with low-frequency reciprocating motion, and uses the periodic elliptical vibration generated by a two-dimensional ultrasonic vibration device working in a resonant state to form an elliptical trajectory, thereby improving the machinability during the removal of difficult-to-process materials, and further realizing high-precision processing of optical free-form surfaces on difficult-to-process materials.

[0022] (2) The present invention adopts an integrated design and combined working mode of a non-resonant vibration device and a two-dimensional ultrasonic vibration device. Compared with a dual-frequency vibration modulation cutting device with a separate design, it reduces the assembly error and the influence of the separate design on the resonant frequency, and solves the problems of difficulty in coupling, low processing efficiency, poor processing accuracy and difficulty in driving and controlling a single vibration device using low / high frequency current drive. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic structural diagram of a resonant and non-resonant integrated dual-frequency vibration modulation cutting device provided by an embodiment of the present invention;

[0024] Figure 2 yes Figure 1 A top view of

[0025] Figure 3 is a schematic structural diagram of a two-dimensional ultrasonic vibration device in an embodiment of the present invention;

[0026] Figure 4 is a schematic diagram of the arrangement of piezoelectric ceramics in an embodiment of the present invention;

[0027] Figure 5 It is a schematic diagram of the tool trajectory generation principle of dual-frequency vibration modulation in an embodiment of the present invention. DETAILED DESCRIPTION

[0028] The present invention will be further described below in conjunction with the accompanying drawings.

[0029] Attached Figures 1 to 5 The reference numerals in the figures are as follows:

[0030] 1, non-resonant vibration device; 11, flexible hinge mechanism; 12, piezoelectric ceramic stack; 13, frame; 14, Z-axis direction pre-tightening screw; 15, bolt hole;

[0031] 2, two-dimensional ultrasonic vibration device; 21, ultrasonic amplitude transformer; 22, ultrasonic transducer; 221, front cover; 222, bending vibration type piezoelectric ceramic group; 223, longitudinal vibration type piezoelectric ceramic; 224, rear cover; 225, flange support structure; 23, pre-tightening bolt;

[0032] 3. Cutting tools.

[0033] In the description of the present application, it should be noted that the terms "front", "rear", "left", "right", etc., indicating directions or positional relationships, are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as a limitation on the present application.

[0034] like Figure 1 and Figure 2 As shown, the embodiment of the present invention provides a resonant and non-resonant integrated dual-frequency vibration modulation cutting device, which is a front-to-back symmetrical structure (see Figure 2 ), including a non-resonant vibration device 1, a two-dimensional ultrasonic vibration device 2 (resonant vibration device) and a tool 3.

[0035] The non-resonant vibration device 1 includes a flexible hinge mechanism 11, a piezoelectric ceramic stack 12, a frame 13 and a Z-axis pre-tightening screw 14, wherein the frame 13 is U-shaped and the opening faces left. The flexible hinge mechanism 11 is U-shaped, and the two ends of the flexible hinge mechanism 11 are connected to the inner wall of the frame 13 through arc hinges. The number of arc hinges is four, two at each end, and they are distributed at intervals. The opening of the flexible hinge mechanism 11 is also facing left, and the left end faces of the flexible hinge mechanism 11 and the frame 13 are flush. The piezoelectric ceramic stack 12 is located between the flexible hinge mechanism 11 and the frame 13, and the Z-axis pre-tightening screw 14 passes through the frame 13 from the right side and is connected to the threaded connection end of the piezoelectric ceramic stack 12. Bolt holes 15 are provided at the four corners of the frame 13 for connecting to the machine tool guide rails.

[0036] Combination Figure 3 The two-dimensional ultrasonic vibration device 2 includes an ultrasonic horn 21 , an ultrasonic transducer 22 and a pre-tightening bolt 23 . The ultrasonic horn 21 is arranged along the Z-axis direction, and the tool 3 is installed at the front end of the ultrasonic horn 21 .

[0037] The ultrasonic transducer 22 adopts a square cross-section structure, including a front cover plate 221, a bending vibration type piezoelectric ceramic group 222, a longitudinal vibration type piezoelectric ceramic 223 and a rear cover plate 224, wherein the rear cover plate 224 is connected to the inner wall of the flexible hinge mechanism 11 through the flange support structures 225 on both sides thereof. The pre-tightening bolt 23 passes through the rear cover plate 224, the longitudinal vibration type piezoelectric ceramic 223, the bending vibration type piezoelectric ceramic group 222 and the front cover plate 221 in sequence from the center, and is finally fixed to the rear end face of the ultrasonic horn 21.

[0038] In this embodiment, the flexible hinge mechanism 11 (including the arc hinge), the frame 13 and the rear cover plate 224 (including the flange support structure 225) are an integrated structure, which reduces the assembly error caused by the separate design and the impact on the output vibration trajectory accuracy.

[0039] The flexible hinge mechanism 11 has the characteristics of low longitudinal stiffness, high lateral stiffness and low stress concentration, which can improve the ability of the non-resonant vibration device 1 to suppress parasitic motion and other external interferences, constrain the displacement of the device along the X-axis direction, and reduce the parasitic motion in the X-axis direction. The piezoelectric ceramic stack 12 is driven by piezoelectricity. By giving the piezoelectric ceramic stack 12 a low-frequency AC signal, the piezoelectric ceramic stack 12 applies a displacement in the Z-axis direction to the flexible hinge mechanism 11. By means of the bending deformation of the flexible hinge, the flexible hinge mechanism 11 outputs the displacement in the Z-axis direction to the rear cover plate 224 of the ultrasonic transducer 22, thereby applying a low-frequency oscillation in the Z-axis direction to the two-dimensional ultrasonic vibration device 2. The non-resonant vibration device 1 usually works below its natural frequency, is suitable for the requirements of low-frequency vibration, and can ensure the motion accuracy of the device. The device needs to provide a controllable vibration displacement in the Z-axis direction, while providing sufficient force and output stiffness. The piezoelectric ceramic stack 12 is driven by a harmonic or arbitrary excitation signal. By applying a suitable excitation signal, such as a sinusoidal signal, to the actuator, a displacement with variable amplitude and pitch can be generated.

[0040] The working principle of the piezoelectric ceramics in the ultrasonic transducer 22 is based on the inverse piezoelectric effect, which means that when an electric field is applied in the polarization direction of the dielectric, these dielectrics will produce mechanical deformation or mechanical pressure in a certain direction. Figure 4 Since the amplitude capacity of bending vibration is weaker than that of longitudinal vibration, 4 semi-square piezoelectric ceramics are selected to form a bending vibration ceramic group, and 2 square piezoelectric ceramics are selected to form a longitudinal vibration ceramic group.

[0041] The longitudinal vibration type piezoelectric ceramic 223 is composed of two stacked piezoelectric ceramic square pieces, and the longitudinal vibration of the ultrasonic transducer 22 is generated by the longitudinal elongation and contraction deformation of the longitudinal vibration type piezoelectric ceramic 223. The bending vibration type piezoelectric ceramic group 222 is composed of two groups of half-square piezoelectric ceramics, and each group of bending vibration type piezoelectric ceramics is composed of two piezoelectric ceramic half-square pieces with opposite polarization directions. When a high-frequency signal is applied to the piezoelectric ceramic, one half-square piece is stretched and the other half-square piece is compressed, so that the piezoelectric ceramic generates a bending moment, thereby generating bending vibration of the ultrasonic transducer 22, and then the longitudinal vibration formed by the longitudinal vibration type piezoelectric ceramic 223 and the bending vibration formed by the bending vibration type piezoelectric ceramic group 222 are combined to generate elliptical vibration.

[0042] The two-dimensional ultrasonic vibration device 2 is arranged in an O-XYZ coordinate system, and the Y axis and the Z axis are as follows: Figure 4 As shown, the X axis is determined according to the right-hand rule. The longitudinal vibration type piezoelectric ceramic 223 can generate longitudinal vibration deformation in the Z-axis direction, and the bending vibration type piezoelectric ceramic group 222 can generate bending vibration deformation in the Y-axis direction. During the free-form surface machining process, the tool 3 contacts the workpiece to achieve material removal.

[0043] The embodiment of the present invention also provides a cutting method of the resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to the embodiment of the present invention, comprising:

[0044] When in use, in the Y-axis and Z-axis directions, the tool 3 is driven by the ultrasonic vibration frequency f1 with a certain phase difference in two directions generated by the two-dimensional ultrasonic vibration device 2, which can form an elliptical vibration trajectory in a two-dimensional space, which is used to improve the machinability during material removal. In addition, the tool 3 is affected by the low-frequency oscillation f2 with a large amplitude generated by the non-resonant vibration device 1 in the Z-axis direction, realizing the creation of a free-form surface contour. By coupling high-frequency ultrasonic elliptical vibration with low-frequency oscillation, dual-frequency vibration modulation of the tool 3 relative to the workpiece is realized, and the tool's motion trajectory is as follows: Figure 5 shown.

[0045] The present invention utilizes a non-resonant vibration device to generate low-frequency vibrations in the dual-frequency vibration modulation cutting process to achieve the creation of a free-form surface contour, and utilizes an ultrasonic elliptical vibration generated by a two-dimensional ultrasonic vibration device (resonant vibration device) to improve the machinability in the material removal process, thereby achieving high-precision processing of optical free-form surfaces on difficult-to-process materials.

Claims

1. A resonant and non-resonant integrated dual-frequency vibration modulation cutting device, characterized in that: The overall structure is symmetrical front and back, and includes a non-resonant vibration device (1) and a two-dimensional ultrasonic vibration device (2); The non-resonant vibration device (1) comprises a flexible hinge mechanism (11), a piezoelectric ceramic stack (12), a frame (13) and a Z-axis direction pre-tightening screw (14); the frame (13) is U-shaped with an opening facing left; the flexible hinge mechanism (11) is U-shaped, and both ends of the flexible hinge mechanism (11) are connected to the inner wall of the frame (13), and the opening is also facing left; the piezoelectric ceramic stack (12) is located between the flexible hinge mechanism (11) and the frame (13); the Z-axis direction pre-tightening screw (14) passes through the frame (13) from the right side and is connected to the threaded connection end of the piezoelectric ceramic stack (12); The two-dimensional ultrasonic vibration device (2) comprises an ultrasonic amplitude transformer (21) arranged along the Z-axis direction, a tool (3) is installed at the front end of the ultrasonic amplitude transformer (21), and an ultrasonic transducer (22) is installed at the rear end; the rear cover plate (224) of the ultrasonic transducer (22) is connected to the inner wall of the flexible hinge mechanism (11) through a flange support structure (225); the flexible hinge mechanism (11), the frame (13) and the rear cover plate (224) are an integrated structure; the piezoelectric ceramic stack (12) is used to apply a displacement in the Z-axis direction to the flexible hinge mechanism (11), and the flexible hinge mechanism (11) is used to output the displacement in the Z-axis direction to the two-dimensional ultrasonic vibration device (2).

2. The resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to claim 1 is characterized in that: The ultrasonic transducer (22) adopts a square cross-section structure and comprises a bending vibration type piezoelectric ceramic group (222) and a longitudinal vibration type piezoelectric ceramic (223). The bending vibration type piezoelectric ceramic group (222) is used to generate bending vibration in the Y-axis direction, and the longitudinal vibration type piezoelectric ceramic (223) is used to generate longitudinal vibration in the Z-axis direction.

3. The resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to claim 2, characterized in that: The bending vibration type piezoelectric ceramic group (222) is composed of two groups of semi-square piezoelectric ceramics, and each group of bending vibration type piezoelectric ceramics is composed of two piezoelectric ceramic semi-square pieces with opposite polarization directions.

4. The resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to claim 2, characterized in that: The longitudinal vibration type piezoelectric ceramic (223) is composed of two stacked piezoelectric ceramic square sheets.

5. The resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to claim 2, characterized in that: The ultrasonic horn (21) and the ultrasonic transducer (22) are fixed by means of a pre-tightening bolt (23).

6. The resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to claim 5, characterized in that: The ultrasonic transducer (22) also includes a front cover plate (221), and the pre-tightening bolt (23) passes through the rear cover plate (224), the longitudinal vibration type piezoelectric ceramic (223), the bending vibration type piezoelectric ceramic group (222) and the front cover plate (221) in sequence, and is finally fixed to the rear end surface of the ultrasonic horn (21).

7. The resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to claim 1, characterized in that: The frame (13) is provided with bolt holes (15) for connecting with the guide rails of a machine tool.

8. The resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to claim 1, characterized in that: The flexible hinge mechanism (11) is integrally connected to the frame (13) via an arc-shaped hinge.

9. The resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to claim 1, characterized in that: The left end surfaces of the frame (13) and the flexible hinge mechanism (11) are flush with each other.

10. A cutting method of the resonant and non-resonant integrated dual-frequency vibration modulation cutting device according to any one of claims 1 to 9, characterized in that: In the Y-axis and Z-axis directions, the tool (3) is driven by ultrasonic vibration frequencies f1 with a certain phase difference in two directions generated by a two-dimensional ultrasonic vibration device (2), forming a two-dimensional elliptical vibration trajectory, which is used to improve the machinability during the material removal process; the tool (3) is acted on by a large-amplitude low-frequency oscillation f2 generated by a non-resonant vibration device (1) in the Z-axis direction, thereby achieving the creation of a free-form surface contour; and dual-frequency vibration modulation of the tool (3) relative to the workpiece is achieved through the coupling of high-frequency ultrasonic elliptical vibration and low-frequency oscillation.

Citation Information

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