A non-linear energy sink device for cutting chatter passive control

Abstract

The application discloses a kind of non-linear energy sink devices for cutting chatter passive control, utilize target energy transmission mechanism to target transmission cutting vibration energy into non-linear energy sink, carry out wide-frequency vibration control, including mass, linear stiffness beam, permanent magnet, super material damping element, outer frame and cover plate;Mass is the cylindrical body of metal conductor material, three different sizes of linear stiffness beam respectively pass through the three through holes of mass, with the increase of amplitude, 3 sections of linear stiffness can be obtained, segmented linear stiffness can be fitted approximately as nonlinear cubic stiffness;Super material damping element is fixed between outer frame and mass, and friction and viscous damping are generated by vibration extrusion stretching;Permanent magnet is fixed on the bottom surface of cover plate, and eddy current damping is generated between conductor mass during vibration.The application is small in size, structure is closed, and is convenient to apply in cutting system, has the characteristics of targeted energy transmission, and has good effect of inhibiting cutting chatter.

Description

Technical Field

[0001] This invention belongs to the field of machining and relates to a nonlinear energy trap device for passive control of cutting chatter. Background Technology

[0002] During metal cutting, chatter can reduce the precision and surface quality of machined parts, and may even damage the machine tool spindle and cutting tools. To suppress chatter, various vibration dampers are used in cutting systems. Vibration dampers are generally classified into active, semi-active, and passive types. Active and semi-active vibration dampers have good vibration suppression effects, but require corresponding hardware and software equipment, resulting in high costs and limitations in practical applications. Passive vibration dampers, on the other hand, have advantages such as simple structure, convenient implementation, and low cost, and are widely used in cutting processes.

[0003] Passive vibration dampers can be divided into linear and nonlinear types. Among linear vibration dampers, tuned dampers are widely used. They typically consist of a mass block, a spring, and damping units. By attaching them to the main structure and adjusting the damper's natural frequency to match that of the main structure, a good vibration reduction effect is achieved. Chinese patent CN101839302B proposes an elastically supported dry friction tuned mass damper for cutting chatter control. This single-degree-of-freedom damper uses a cantilever beam structure damper oscillator combined with a double-layer elastic friction plate. By adjusting its natural frequency to near the fundamental frequency of the cutting system, it can effectively reduce system vibration. However, its vibration reduction effect is greatly affected by the characteristics of the main system and external excitation. When the damper's natural vibration frequency deviates from the fundamental frequency of the main system, or when the external excitation frequency exceeds its effective tuning bandwidth, the vibration reduction effect is poor. Chinese patent CN104819233B proposes a two-degree-of-freedom eddy current tuned passive damper, mainly comprising a mass block, a support frame, a cylindrical rod, a stiffness adjusting nut, a permanent magnet, and a support plate. It utilizes eddy current damping between the mass block and the permanent magnet to dissipate cutting vibration energy. Furthermore, the stiffness and damping parameters can be tuned separately. Compared to a single-degree-of-freedom tuned damper, its vibration reduction effect and robustness are improved, and it can suppress the first or second-order modes of the cutting system. However, since linearly tuned dampers can only achieve good vibration reduction within a specific frequency band, they have certain limitations in practical applications.

[0004] Nonlinear energy traps, developed from tuned mass dampers, have received extensive research attention both domestically and internationally. They primarily consist of a nonlinear stiffness spring, a damper, and a mass block. Nonlinear energy traps possess targeted energy transfer characteristics, enabling the unidirectional and irreversible transfer of vibration energy from the main system to the nonlinear energy trap, thus achieving better vibration reduction. Furthermore, due to the presence of nonlinear stiffness, nonlinear energy traps can reduce vibration over a wide frequency range without the need for tuning parameters. During machining processes, as material is removed, the structural modal parameters of the part change; the wide-frequency vibration reduction characteristics of the nonlinear energy trap enable it to better suppress chatter.

[0005] Chinese patent CN106059392B proposes a self-powered, integrated active-passive nonlinear vibration control device for the entire satellite. It uses cubic stiffness springs, damping materials, and mass blocks as nonlinear energy traps applied to the entire satellite system, achieving good vibration reduction. However, to obtain certain nonlinear stiffness and damping coefficients, the traditional cubic stiffness springs and damping materials used have large structures, making them unsuitable for closed system environments, especially for machining systems. Chinese patent application CN112160437A designs a bidirectional eddy current nonlinear energy trap vibration reduction device, applied in the field of structural engineering vibration control technology. Chinese patent CN110681700B proposes a nonlinear energy trap device that uses magnetorheological fluid to change stiffness, used to alter the stiffness characteristics of rolling mills, thereby obtaining higher quality rolled plates. Chinese patent CN113982344B utilizes multiple permanent magnets combined with guide rails to design a magnetic nonlinear energy trap structure, achieving vibration absorption and energy dissipation of structural vibrations in a two-dimensional plane. All these devices suffer from large size, making them difficult to widely apply in machining processes. Chinese patent application CN115021616A designs a simple and easy-to-install nonlinear energy trap structure using piecewise linear spring assemblies with different spring stiffness combinations and numbers. The nonlinear stiffness primarily depends on the size of each spring. Chinese patent CN110230661B proposes a nonlinear energy trap with piecewise linear beams for use in rotor systems. It mainly includes a mass block and horizontal piecewise linear beams. The piecewise linear beams approximate cubic stiffness, reducing the volume of the nonlinear energy trap and effectively reducing rotor system vibration. However, its damping is the self-damping of the piecewise linear beams, resulting in a small damping coefficient and limiting vibration energy dissipation. Chinese patent CN109505922B designs a multistable nonlinear energy trap with piecewise linear beams and permanent magnet negative stiffness. It uses a vertical three-segment linear beam to generate nonlinear positive stiffness and internal and external magnets to provide negative stiffness. The combination of positive and negative stiffness effectively suppresses transient vibrations. However, this device also suffers from small self-damping, limiting vibration energy dissipation. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a nonlinear energy trap device for passive control of cutting chatter. This device reduces vibration in the tool or workpiece system during cutting. It is a closed-loop, adjustable-damping nonlinear energy trap device that can effectively passively suppress cutting chatter over a wide frequency range. Nonlinear stiffness is achieved through a structural design of three linear stiffness beams and a mass block, replacing traditional nonlinear springs. Furthermore, the use of eddy current damping and metamaterial damping elements effectively reduces the volume of the nonlinear energy trap, improves the system's vibration energy dissipation capability, and, due to its enclosed structure, is unaffected by cutting fluid and chips, making it more suitable for application in cutting systems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A nonlinear energy trap device for passive control of cutting chatter includes a mass block, linear stiffness beams, permanent magnets, metamaterial damping elements, an outer frame, and a cover plate. The mass block is cylindrical with three rectangular through holes on its surface. The length and width of the three rectangular through holes are different, representing large, medium, and small holes. The linear stiffness beams have three different widths but the same thickness. The narrowest linear stiffness beam passes through the narrowest through hole below the mass block and is seamlessly fitted and fixed to the mass block. The other two linear stiffness beams are suspended and pass through the other two through holes. The two ends of the three linear stiffness beams are fixed to the outer frame. The permanent magnet is fixed to the bottom surface of the cover plate with epoxy resin adhesive. The metamaterial damping element is fixed to the inner side of the outer frame with epoxy resin adhesive on one side and to the surface of the mass block with the other side on the other side. The outer frame is cylindrical with three rectangular slots for mounting the linear stiffness beams. The cover plate is mounted on the outer frame.

[0009] Furthermore, the narrowest linear stiffness beam is seamlessly fitted and fixed to the mass block, and supports the mass block. The other two linear stiffness beams, which are suspended through the mass block, have certain gaps with the hole wall around them. The gap between the widest linear stiffness beam and the hole wall in the vertical direction is larger than the gap between the other linear stiffness beam and the hole wall in the vertical direction.

[0010] Furthermore, the linear stiffness beam is made of silicon-manganese alloy spring steel.

[0011] Furthermore, the metamaterial damping element is a structured lattice metamaterial with Coulomb friction damping and viscous damping characteristics.

[0012] Furthermore, the mass block is made of a metallic conductor, and when vibration occurs between it and the permanent magnet, the radial magnetic flux change generates eddy current damping.

[0013] Furthermore, the gaps between the other two linear stiffness beams suspended through the mass block and the mass block are different. When vibration occurs, as the amplitude increases, three segments of linear stiffness can be obtained. The segmented linear stiffness can be approximated as a nonlinear cubic stiffness.

[0014] Furthermore, the permanent magnet can be made of different diameters and thicknesses to adjust the magnitude of the eddy current damping.

[0015] Furthermore, as a passive, locally attached nonlinear energy absorber, it captures the cutting vibration energy of the cutting system over a wide frequency range and targets and transfers the cutting vibration energy to the nonlinear energy trap device, converting it into corresponding kinetic and potential energy. Then, the energy is dissipated through damping, thereby achieving wide-frequency passive suppression of cutting chatter.

[0016] The working principle of this invention is as follows:

[0017] This nonlinear energy trap device is small in size and can be installed on cutting system structures such as cutting tools or workpieces. When cutting vibration occurs, the cutting vibration energy is targeted to the nonlinear energy trap device using a target energy transfer mechanism. It can capture cutting vibration energy in a wide frequency range in real time and dissipate the captured vibration energy in real time through damping. The entire energy transfer process is irreversible, which can more effectively and passively suppress cutting vibration.

[0018] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0019] (1) Due to its targeted energy transfer characteristics, the nonlinear energy trap device of the present invention can better absorb and dissipate vibration energy. Its nonlinear characteristics can passively suppress cutting chatter over a wide frequency range, and its vibration reduction frequency range is wider than that of existing tuned mass dampers.

[0020] (2) The nonlinear energy trap device of the present invention obtains nonlinear stiffness through the structural design of three linear stiffness beams and mass blocks, replacing the traditional nonlinear spring. At the same time, it adopts eddy current damping and metamaterial damping elements, which greatly reduces the volume of the nonlinear energy trap and solves the limitations of the traditional nonlinear energy trap being too large and inconvenient to install in the cutting system.

[0021] (3) The nonlinear energy trap device of the present invention is easy to install and disassemble, and its damping can be adjusted by using permanent magnets of different diameters and thicknesses.

[0022] (4) The nonlinear energy trap device of the present invention has a closed structure and will not be affected by cutting fluid or chips when applied in a cutting system. Attached Figure Description

[0023] The accompanying drawings are provided to further illustrate the invention and constitute a part of this invention. The following illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute a limitation thereof.

[0024] Figure 1 This is an overall diagram of the nonlinear energy trap device of the present invention;

[0025] Figure 2 This is an internal structural diagram of the nonlinear energy trap device of the present invention;

[0026] Figure 3 This is a diagram of the mass block in the nonlinear energy trap device of the present invention;

[0027] Figure 4 This is a schematic diagram illustrating the application of the nonlinear energy trap device of the present invention in milling thin-walled workpieces;

[0028] Figure 5 This is a dynamic model diagram of the milling system using a nonlinear energy trap device in the embodiment;

[0029] In the figure: 1. Mass block; 2. Linear stiffness beam; 3. Permanent magnet; 4. Metamaterial damping element; 5. Outer frame; 6. Cover plate; 7. Fixture; 8. Nonlinear energy trap device; 9. Cutting tool; 10. Workpiece. Detailed Implementation

[0030] The embodiments of the disclosed examples of the present invention will now be described in detail with reference to the accompanying drawings, clearly indicating the purpose, technical solution, and advantages of the present invention. It should be noted that the following detailed descriptions of the embodiments are exemplary.

[0031] An embodiment of the present invention provides a nonlinear energy trap device for passive control of cutting chatter, such as... Figure 1 , Figure 2 , Figure 3 As shown, the nonlinear energy trap device may include a mass block 1, a linear stiffness beam 2, a permanent magnet 3, a metamaterial damping element 4, an outer frame 5, and a cover plate 6.

[0032] Preferably, the mass block 1 can be made of copper; the linear stiffness beam 2 is made of silicon-manganese alloy spring steel 60Si2Mn; the permanent magnet 3 is a neodymium magnet; the metamaterial damping element 4 is a structured lattice metamaterial; and the outer frame 5 and the cover plate 6 are made of resin. Three linear stiffness beams 2 of different widths pass through three through holes in the mass block 1, with the smallest lower linear stiffness beam 2 seamlessly fitted and fixed to the through hole of the mass block 1. The other two linear stiffness beams 2 have certain gaps between themselves and the walls of the holes they pass through. The largest upper linear stiffness beam 2 has a larger gap in the vertical direction between itself and the hole wall than the middle linear stiffness beam 2 has. The two ends of the three linear stiffness beams 2 are fixed to the walls of the outer frame 5. The metamaterial damping element 4 is installed on the surfaces of the outer frame 5 and the mass block 1 using epoxy resin adhesive. The permanent magnet 3 is fixed to the bottom surface of the cover plate 6 using epoxy resin adhesive.

[0033] When the mass block 1 does not vibrate or the amplitude is small, only the lower linear stiffness beam 2 exerts a force on the mass block 1. When the amplitude of the mass block 1 increases, the two originally suspended linear stiffness beams 2 will successively contact the upper and lower walls of the through hole of the mass block 1 and exert a force. That is, as the amplitude increases, the three linear stiffness beams 2 can generate three segments of linear stiffness, and the three segments of linear stiffness can be approximated as a nonlinear cubic stiffness.

[0034] When vibration occurs, eddy current damping is generated between the permanent magnet 3 and the mass block 1. The metamaterial damping element 4 is subjected to compression and stretching by the mass block 1 and the outer frame 5, generating Coulomb friction damping and viscous damping. The magnitude of the eddy current damping can be adjusted by selecting neodymium magnets of different diameters and thicknesses.

[0035] like Figure 4 As shown, in a thin-walled workpiece milling system, the two ends of the thin-walled workpiece are fixed on the fixture 7, and the upper surface of the workpiece 10 is milled by a cutting tool 9. A nonlinear energy trap device 8 is installed on the lower surface of the workpiece 10 being machined. The cutting tool 9 can be a milling cutter. The workpiece 10 can be a thin-walled workpiece.

[0036] In this embodiment, the thin-walled workpiece is a flexible workpiece, the tooling system is weakly rigid, and the nonlinear energy trap device is installed below the thin-walled workpiece. The system dynamics model is as follows: Figure 5 As shown, the dynamic equation can be expressed as:

[0037]

[0038] , , Cutting tools x Modal mass, damping, and stiffness coefficients in the directional direction; , , Cutting tools y Orientational modal mass, damping, and stiffness coefficients;

[0039] , , Thin-walled workpieces x Modal mass, damping, and stiffness coefficients in the directional direction; , , Thin-walled workpieces y Orientational modal mass, damping, and stiffness coefficients;

[0040] , , These represent the mass, total damping coefficient, and fitted nonlinear stiffness coefficient of the nonlinear energy trap device, respectively.

[0041] and For the knife in x and y Vibration displacement in the direction; and For thin-walled workpieces x and y Vibration displacement in the direction; For nonlinear energy trap mass blocks in y Vibration displacement in the direction;

[0042] and for x and y Cutting force in the direction:

[0043]

[0044] in This refers to the axial cutting depth of the tool. This indicates that the time delay is one period, and N is the number of milling cutter teeth. The spindle speed of the machine tool; , , and This is the dynamic cutting force coefficient.

[0045] Because the system equations contain nonlinear terms, specifically cubic terms, linearization is required before calculating the stability domain of chatter. The nonlinear terms are expanded around the equilibrium point, whose value is obtained from the system's periodic solution. The nonlinear equations require bifurcation points to obtain the periodic solution. The expansion of the nonlinear terms at the equilibrium point is as follows:

[0046]

[0047] in and This represents the equilibrium point value.

[0048] Substitute this into the system equations and transform it into a space state form:

[0049]

[0050] in The superscript T indicates the transpose of the matrix;

[0051] and It is a 10th order square matrix:

[0052] ;

[0053] in

[0054]

[0055]

[0056]

[0057] in

[0058] , , ,

[0059] Next, the semi-discrete method is used to calculate the flutter stability region, dividing each period T into n periods. The delayed term can be transformed into:

[0060]

[0061] in , , Substituting the above equation into the system's spatial state equation yields the semi-discretized spatial state equation, where the subscript n denotes the number of discrete elements:

[0062]

[0063] The solution to the above equation can be set as:

[0064]

[0065] Substituting into the above formula ,at the same time , It can be represented as:

[0066]

[0067] This series of equations can be expressed as follows over the discrete time interval:

[0068]

[0069] in for vector, for Square matrix.

[0070]

[0071]

[0072] The transfer matrix of the cutter tooth response in adjacent periods of the milling dynamics system can then be obtained. :

[0073]

[0074] According to Floquet theory, if the transfer matrix If the magnitude of the largest eigenvalue is greater than 1, the milling system is determined to be stable, and thus the improved flutter stability domain of the system after adding a nonlinear energy trap is obtained.

[0075] The thin-walled workpiece is made of 7075 aluminum alloy, with specific dimensions of 3*100*150mm. The cutting tool is a 12mm diameter 4-tooth carbide end mill. The specific experimental steps are as follows:

[0076] The first step is to conduct modal testing on the milling system and determine its modal parameters. A hammer excitation method is used, where a hammer strikes the milling cutter mounted on the machine tool to generate an excitation force signal. The response signal of the milling cutter is acquired using an accelerometer, and the transfer function is obtained through FFT analysis using a dual-channel data acquisition and analysis instrument. Finally, the modal analysis software Model Genius is used to obtain the modal parameters of the milling system. x and y Modal parameters such as modal mass, modal stiffness, and modal damping in both directions.

[0077] The second step involves conducting modal tests on thin-walled workpieces mounted with fixtures to obtain the performance of the workpiece-fixture system. x and y Modal parameters in two directions. The modal testing procedure is the same as in the first step.

[0078] The third step is to measure the three-dimensional cutting force coefficient of the milling cutter through a cutting force experiment. First, the three-dimensional force gauge is horizontally mounted on the machine tool worktable. Then, the thin-walled workpiece is mounted on the force gauge, and milling is performed on the thin-walled workpiece. The three-dimensional force gauge can obtain the three-dimensional cutting force signal during the milling process, and the cutting force coefficient is obtained by analyzing it with the software Dyno Ware.

[0079] The fourth step involves substituting the parameters obtained from the modal tests and cutting force tests into the system dynamics model, and then deriving the transfer matrix. The formula calculates the system stability lobe diagram of the milling system without the nonlinear energy trap device, and then calculates the system stability lobe diagram with the nonlinear energy trap device. The system stability domain is significantly increased after the nonlinear energy trap device is installed.

[0080] The fifth step involves comparing the system stability domains before and after installing the nonlinear energy trap device. Within the increased stability domain, multiple sets of different rotational speeds and depths of cut parameters are selected to conduct milling experiments on thin-walled workpieces with and without the nonlinear energy trap device. A vibration acceleration sensor is installed on the thin-walled workpiece... x and y The vibration response during milling was obtained through a data acquisition system, and the amplitude of the vibration acceleration response was significantly reduced after the installation of the nonlinear energy trap device.

[0081] Step 6: After the thin-walled workpiece is milled, observe the surface quality of multiple groups of machined workpieces under the same cutting parameters. The workpiece without the nonlinear energy trap device has obvious surface texture and chatter occurred during the machining process, while the workpiece with the nonlinear energy trap device has a smooth surface and no chatter occurred.

[0082] Step 7, using H ∞ The criteria determine the optimal parameters of the nonlinear energy trap damping. The magnitude of the eddy current damping is adjusted by selecting neodymium magnets with different diameters and thicknesses, and a new stability lobe diagram of the system is calculated. The results are then verified by repeating the above milling experiments.

[0083] The specific embodiments of the present invention described above are not intended to limit the scope of protection of the present invention. Any modifications or substitutions made to the above-described device of the present invention based on the above-described content of the present invention, using common techniques and methods in the field, without departing from the basic technical concept of the present invention, shall be within the scope of protection of the present invention.

Claims

1. A nonlinear energy trap device for passive control of cutting chatter, characterized in that: It includes a mass block (1), a linear stiffness beam (2), a permanent magnet (3), a metamaterial damping element (4), an outer frame (5), and a cover plate (6); The mass block (1) is a cylinder with three rectangular through holes on its surface. The length and width of the three rectangular through holes are different, and they are divided into three holes: large, medium and small. The linear stiffness beam (2) has three different width specifications, with the same thickness. The linear stiffness beam (2) with the smallest width passes through the smallest through hole below the mass block (1) and is seamlessly attached and fixed to the mass block (1). The other two linear stiffness beams (2) are suspended and pass through the other two through holes respectively. The two ends of the three linear stiffness beams (2) are fixed to the outer frame (5) respectively. The permanent magnet (3) is fixed to the bottom surface of the cover plate (6) by epoxy resin adhesive; The metamaterial damping element (4) is fixed to the inner side of the outer frame (5) with one side by epoxy resin adhesive and to the surface of the mass block (1) with the other side. The outer frame (5) is cylindrical in shape and has three rectangular slots on it for installing linear stiffness beams (2). The cover plate (6) is installed on the outer frame (5). The linear stiffness beam (2) with the smallest width supports the mass block (1). The other two linear stiffness beams (2) that are suspended through the mass block (1) have certain gaps around the hole wall. The gap between the linear stiffness beam (2) with the largest width and the hole wall in the vertical direction is larger than the gap between the other linear stiffness beam (2) and the hole wall in the vertical direction. The mass block (1) is made of metal conductor material. When it vibrates with the permanent magnet (3), the radial magnetic flux changes and eddy current damping is generated.

2. The nonlinear energy trap device for passive control of cutting chatter according to claim 1, characterized in that: The linear stiffness beam (2) is made of silicon manganese alloy spring steel.

3. A nonlinear energy trap device for passive control of cutting chatter according to claim 1, characterized in that: The metamaterial damping element (4) is a structured lattice metamaterial with Coulomb friction damping and viscous damping characteristics.

4. A nonlinear energy trap device for passive control of cutting chatter according to claim 1, characterized in that: The vertical gap between the two linear stiffness beams (2) that are suspended through the mass block (1) and the mass block (1) has different dimensions. When vibration occurs, as the amplitude increases, three segments of linear stiffness can be obtained. The segmented linear stiffness can be approximated as a nonlinear cubic stiffness.

5. A nonlinear energy trap device for passive control of cutting chatter according to claim 1, characterized in that: The permanent magnet (3) is made of different diameters and thicknesses to adjust the magnitude of eddy current damping.

6. A nonlinear energy trap device for passive control of cutting chatter according to any one of claims 1-5, characterized in that: As a passive, locally attached nonlinear energy absorber, the nonlinear energy trap device captures the cutting vibration energy of the cutting system over a wide frequency range and targets and transfers the cutting vibration energy to the nonlinear energy trap device, converting it into corresponding kinetic and potential energy. The energy is then dissipated through damping, thereby achieving wide-frequency passive suppression of cutting chatter.

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