Design optimization method of vibration-damping grinding rod and vibration-damping grinding rod

Abstract

The present invention relates to a design optimization method for a vibration-damping grinding rod and a vibration-damping grinding rod. The method analyzes a constructed three-dimensional structural model of the vibration-damping grinding rod using finite element analysis software, constructs a mathematical model based on the analyzed data, and optimizes the vibration-damping grinding rod based on the mathematical model. The present invention also provides an optimized vibration-damping grinding rod that can effectively improve the dynamic performance of the vibration-damping grinding rod, reduce vibration caused by chatter, thereby reducing surface roughness during machining and improving the dimensional accuracy of the machined surface. Furthermore, the vibration-damping grinding rod optimization method provided by the present invention is highly versatile and can be applied to optimize vibration-damping grinding rods of any structure.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical structure design, and in particular to a design optimization method for a vibration-damping grinding rod and the vibration-damping grinding rod. Background Art

[0002] In industries like aviation, aerospace, and defense, hole machining accounts for up to 33% of metalworking operations. Among these processes, the most challenging is machining the inner surfaces of deep holes with large aspect ratios, such as those found in various long shafts in aerospace equipment, gun barrels in weapons, and various long-stroke hydraulic cylinders. To achieve high machining accuracy and surface finish on these interior surfaces, especially for high-hardness materials, grinding is currently the most common method.

[0003] Due to machining constraints, grinding internal surfaces with large aspect ratios requires a grinding wheel with a large aspect ratio, resulting in low stiffness. Research has shown that when the aspect ratio of the grinding rod is less than 4, the vibration amplitude is low, resulting in high workpiece surface quality. However, when the aspect ratio is greater than 4 but less than 10, more pronounced vibration occurs. The vibration amplitude increases by over 70% with an aspect ratio of 12 compared to an aspect ratio of 10. The primary cause of chatter is the decrease in grinding rod stiffness as the aspect ratio increases. However, in the machining of some deep, small holes, the aspect ratio cannot be reduced due to space constraints. Furthermore, to ensure sufficient grinding linear speed, the grinding spindle speed is typically high. Consequently, chatter is highly likely to occur during the grinding of deep holes with large aspect ratios, leading to the appearance of vibration marks on the ground surface, which compromises surface roughness and dimensional accuracy. Currently, the large aspect ratio of grinding rods has become a key limitation in the machining of high-precision, large-aspect-ratio internal surfaces. Summary of the Invention

[0004] The present invention overcomes the deficiencies of the prior art and provides a design optimization method for a vibration-damping grinding rod.

[0005] A design optimization method for a vibration-damping grinding rod comprises the following steps:

[0006] S1. Constructing a three-dimensional structural model of the vibration-damping grinding rod, wherein the three-dimensional structural model at least includes a damping core layer, a carbon fiber layer, and a metal outer shell layer of the vibration-damping grinding rod;

[0007] S2. Performing static, modal and harmonic response simulation analysis on the three-dimensional structural model using finite element analysis software to obtain data on static stiffness, natural frequency, dynamic stiffness and maximum stress of the vibration-damping grinding rod with different shell materials;

[0008] S3. Optimizing the three-dimensional structural model using static parameters to obtain the static stiffness and damping ratio of the three-dimensional structural model, and establishing a static model related to the static stiffness and damping ratio;

[0009] S4, optimizing the structural parameters of the three-dimensional structural model, establishing a mathematical model of the radius of the damping core layer and a mathematical model of the thickness of the metal shell, and optimizing the vibration-damping grinding rod according to the mathematical models;

[0010] S5. According to the established mathematical model and in combination with the static stiffness, natural frequency, dynamic stiffness and maximum stress, the vibration-damping grinding rod after design optimization is obtained.

[0011] Furthermore, the step S2 is specifically as follows:

[0012] S201, establish a finite element model, define model material parameters, apply loads and boundary conditions, and divide the mesh;

[0013] S202, performing static, modal and harmonic response simulation analysis on the three-dimensional structural model using finite element analysis software;

[0014] S203. Obtain data on static stiffness, natural frequency, dynamic stiffness, and maximum stress of vibration-damping grinding rods with different shell materials.

[0015] Furthermore, the statics model in step S3 is shown in formula (1) to formula (3):

[0016]

[0017] (ρA) equiv =ρ1A1+ρ2A2+ρ3A3 (2)

[0018] Where, is the equivalent density of the vibration reduction grinding rod cross section, ρ i A i is the product of the density and area of ​​the i-th layer of material, F(y,t) is the external force applied to the vibration-damping grinding rod during the grinding process, η is the damping ratio coefficient of the overall structure of the vibration-damping grinding rod, (EI) equiv It is the equivalent bending stiffness of the vibration-damping grinding rod, which is equal to the sum of the bending stiffness of the damping core, carbon fiber layer and metal shell layer.

[0019] The static stiffness k of the grinding rod is expressed as formula (3):

[0020]

[0021] Where j is the number of units in the composite grinding rod, and L is the length of the composite grinding rod.

[0022] Furthermore, in step S201,

[0023] During the process of applying load and constraint, a fixed constraint is applied to the clamping part of the left end face of the vibration-damping grinding rod, and a grinding force is applied at any point on the tip of the grinding wheel.

[0024] Furthermore, the mathematical model of the structural damping ratio coefficient based on the radius of the damping core layer and the thickness of the metal shell layer in step S4 is shown in formula (4) and formula (5):

[0025]

[0026]

[0027] Where T1 is the radius of the damping core layer, T2 is the thickness of the carbon fiber layer, T3 is the thickness of the outer shell layer, and E1, E2, and E3 are the elastic moduli of the three-layer structural materials of the damping core layer, carbon fiber layer, and metal outer shell layer, respectively.

[0028] The present invention also provides a vibration-damping grinding rod, comprising a metal outer shell layer, and also comprising an adhesive layer, a carbon fiber layer, and a damping core layer sequentially arranged in the metal outer shell layer. The vibration-damping grinding rod is a cantilever beam structure.

[0029] Furthermore, the material of the metal shell layer is chromium.

[0030] The present invention provides a design optimization method for a vibration-damping grinding rod and a vibration-damping grinding rod. The optimization method for a vibration-damping grinding rod provided by the present invention is highly versatile and can be applied to optimize vibration-damping grinding rods of any structure. The optimized vibration-damping grinding rod can effectively improve dynamic performance, reduce vibration caused by chatter, and thereby reduce the roughness of the machined surface and improve the dimensional accuracy of the machined surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flow chart of a design optimization method for a vibration-damping grinding rod according to an embodiment of the present invention;

[0032] Figure 2 is a structural diagram of a vibration-damping grinding rod to be optimized in a design optimization method for a vibration-damping grinding rod according to an embodiment of the present invention;

[0033] Figure 3 Schematic diagram of static analysis when 40Cr is used as the metal outer shell layer in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0034] Figure 4 Schematic diagram of harmonic response analysis when 40Cr is used as the metal outer shell layer in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0035] Figure 5 2. It is a structural diagram of a vibration-damping grinding rod optimized into a cantilever beam structure in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0036] Figure 6 1 is a structural schematic diagram of a cross section of a vibration-damping grinding rod in a design optimization method for a vibration-damping grinding rod according to an embodiment of the present invention;

[0037] Figure 7 1 is a schematic diagram of an optimized vibration-damping grinding rod in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0038] FIG8( a ) is a schematic diagram of the maximum static deformation of the all-steel vibration-damping grinding rod in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0039] FIG8( b ) is a schematic diagram of the maximum static deformation of the all-steel vibration-damping grinding rod before optimization in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0040] FIG8( c ) is a schematic diagram of the maximum static deformation of the optimized all-steel vibration-damping grinding rod in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0041] FIG9( a ) is a schematic diagram of the maximum dynamic deformation of the all-steel vibration-damping grinding rod in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0042] FIG9( b ) is a schematic diagram of the maximum dynamic deformation of the all-steel vibration-damping grinding rod before optimization in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention;

[0043] FIG9( c ) is a schematic diagram of the maximum dynamic deformation of the optimized all-steel vibration-damping grinding rod in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention.

[0044] Specific reference numerals include:

[0045] Metal shell layer 1, carbon fiber layer 2, damping core layer 3, nut 4, grinding wheel baffle 5, co-positioning grinding wheel 6, adhesive layer 7. DETAILED DESCRIPTION

[0046] The following is a further detailed description of the embodiments of the present invention in conjunction with the accompanying drawings and examples. It should be noted that the embodiments of the present invention and the features therein can be combined with each other in the absence of conflict. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0047] Figure 1 A flow chart showing a design optimization method for a vibration-damping grinding rod according to an embodiment of the present invention is shown. Figure 2 A structural diagram of a vibration-damping grinding rod to be optimized in a design optimization method for a vibration-damping grinding rod according to an embodiment of the present invention is shown. Figure 3 A schematic diagram of static analysis using 40Cr as the metal outer shell layer in the design optimization method for a vibration-damping grinding rod according to an embodiment of the present invention is shown. Figure 4 A schematic diagram of harmonic response analysis when 40Cr is used as the metal outer shell layer in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention is shown. Figure 5 The structure diagram of the vibration-damping grinding rod optimized into a cantilever beam structure in the design optimization method of the vibration-damping grinding rod according to an embodiment of the present invention is shown. Figure 6 A structural schematic diagram of a cross section of a vibration-damping grinding rod in a design optimization method for a vibration-damping grinding rod according to an embodiment of the present invention is shown. Figure 7 A schematic diagram of the optimized vibration damping grinding rod in the design optimization method for the vibration damping grinding rod according to the embodiment of the present invention is shown. FIG8(a) is a schematic diagram of the maximum static deformation of the all-steel vibration damping grinding rod in the design optimization method for the vibration damping grinding rod according to the embodiment of the present invention. FIG8(b) is a schematic diagram of the maximum static deformation of the all-steel vibration damping grinding rod before optimization in the design optimization method for the vibration damping grinding rod according to the embodiment of the present invention. FIG8(c) is a schematic diagram of the maximum static deformation of the all-steel vibration damping grinding rod after optimization in the design optimization method for the vibration damping grinding rod according to the embodiment of the present invention. FIG9(a) is a schematic diagram of the maximum dynamic deformation of the all-steel vibration damping grinding rod in the design optimization method for the vibration damping grinding rod according to the embodiment of the present invention. FIG9(b) is a schematic diagram of the maximum dynamic deformation of the all-steel vibration damping grinding rod before optimization in the design optimization method for the vibration damping grinding rod according to the embodiment of the present invention. FIG9(c) is a schematic diagram of the maximum dynamic deformation of the all-steel vibration damping grinding rod after optimization in the design optimization method for the vibration damping grinding rod according to the embodiment of the present invention.

[0048] The embodiment of the present invention provides a design optimization method for a vibration-damping grinding rod. Figure 1 As shown, the following steps are included:

[0049] S1. Construct a three-dimensional structural model of the vibration-damping grinding rod. The three-dimensional structural model constructed in the embodiment of the present invention is as follows: Figure 2 As shown, the vibration-damping grinding rod includes a damping core layer, a carbon fiber layer, an outer shell layer, a grinding wheel, a grinding wheel baffle, and a nut. The constructed three-dimensional model of the vibration-damping grinding rod defines that the diameter of the damping core layer of the vibration-damping grinding rod is 2 mm, the thickness of the outer shell is 1.5 mm, and the overall length is 126 mm. That is, the embodiment provided by the present invention is a design optimization method for a vibration-damping grinding rod with a large aspect ratio. The three-dimensional structural model can be constructed based on an existing vibration-damping grinding rod. The embodiment of the present invention does not limit this. The vibration-damping grinding rod to be optimized can be selected according to actual needs.

[0050] S2. Perform static, modal and harmonic response simulation analysis on the three-dimensional structural model using finite element analysis software, and establish a static model of the damping coefficient of the three-dimensional structural model based on the analysis data.

[0051] S201. Establish a finite element model, define model material parameters, apply loads and boundary conditions, and divide the grid; wherein, during the process of applying loads and constraints, a fixed constraint is applied to the clamping portion of the left end face of the vibration-damping grinding rod, and a grinding force is applied at any point on the tip of the grinding wheel.

[0052] S202. Perform static, modal and harmonic response simulation analysis on the three-dimensional structural model using finite element analysis software.

[0053] The technical solutions provided by the embodiments of the present invention are described in detail below with reference to specific embodiments. Table 1 shows common carbon fiber composite substrates in the domestic market. After comprehensively considering the performance and market price of carbon fiber materials, the embodiments of the present invention select A-type carbon fiber composite materials, which have low cost and good modulus and strength, as the substrate for the carbon fiber layer of the vibration-damping grinding rod.

[0054] Table 1 High modulus carbon fiber parameters

[0055]

[0056]

[0057] Table 2 shows the properties of common viscoelastic damping materials. The primary considerations for selection are density, damping ratio, and operating temperature range. Type 1 viscoelastic damping material has a relatively low density, a high damping ratio, and the widest operating temperature range. Therefore, Type 1 was selected as the damping core material for the vibration-damping grinding rod.

[0058] Table 2 Properties of common viscoelastic damping materials

[0059]

[0060]

[0061] In the embodiments provided herein, 40Cr and cemented carbide are used as examples to illustrate the design optimization method for the vibration-damping grinding rod provided herein. As these two materials are the most commonly used for vibration-damping grinding rods, the present invention selects cemented carbide and 40Cr for comparative analysis, from which the more suitable material is selected as the outer shell material for the composite grinding rod. The outer shell can be constructed based on existing vibration-damping grinding rods, and the embodiments of the present invention are not limited thereto. The vibration-damping grinding rod to be optimized can be selected based on actual needs.

[0062] Finite element simulation software was used to perform static, modal and harmonic response simulation analysis on the three-dimensional structural model, and parameters such as the maximum deformation, stress, natural frequency and dynamic stiffness of the vibration-damping grinding rod were obtained. Specifically, it includes: model establishment, material parameter definition, application of loads and boundary conditions, mesh division and solution, and post-processing. Among them, during the load and constraint application process, since the vibration-damping grinding rod is tightly connected to the grinding shaft in the grinding system, a fixed constraint is applied to the clamping part of the left end face of the vibration-damping grinding rod, and a grinding force is applied at a point at the tip of the grinding wheel, where the normal force is 3.4N, the tangential force is 1.8N, and the resultant force is approximately 3.85N.

[0063] exist Figure 3 In the static analysis shown, the normal deformation, tangential deformation, and combined deformation of the vibration-damping grinding rod with 40Cr and cemented carbide outer shell layers are analyzed respectively. The maximum combined deformations are 4.264μm and 3.9874μm respectively, and the maximum deformation difference is 0.27μm. The static stiffnesses are 9.03×107N / m and 9.67×107N / m respectively, and the static stiffness difference is 7%. In the modal analysis, the first-order natural frequency of 40Cr as the metal outer shell layer is 963Hz, while the first-order natural frequency of cemented carbide as the metal outer shell layer is 916Hz. The difference in the first-order natural frequencies is 47Hz, and the natural frequency of the 40Cr outer shell grinding rod is about 5% higher than that of the cemented carbide outer shell grinding rod. Figure 4 In the harmonic response analysis shown, a sinusoidal load of 1.8 N in the tangential direction and 3.4 N in the normal direction, at a frequency of 300 Hz, was applied to the grinding rod (the grinding speed was primarily in the range of 4000 rpm to 18000 rpm). The results show that the maximum deformation and maximum stress of the grinding rod with a 40Cr outer shell are lower than those with a carbide outer shell. The combined maximum radial deformations of the grinding rods with 40Cr and carbide outer shells are 3.8009 μm and 3.8393 μm, respectively, a difference of 0.0384 μm, or 1%. The stresses are 1.7362 MPa and 1.7628 MPa, respectively, a difference of 1.5%. Considering the static stiffness, natural frequency, dynamic stiffness, and maximum stress, 40Cr is the optimal outer shell material for vibration-damping grinding rods with large aspect ratios.

[0064] According to static analysis, modal analysis and harmonic response analysis, it can be found that stress concentration mainly exists at the position where the diameter of the vibration-damping grinding rod and the end suddenly change. Therefore, the existence of fillet can solve the stress concentration phenomenon. This is a detail that needs to be paid attention to in the design of vibration-damping grinding rods with large aspect ratios.

[0065] S3. Establish a statics model of the damping coefficient of the three-dimensional structural model. The statics model is shown in formula (1) to formula (3).

[0066] like Figure 5As shown in the figure, the vibration reduction grinding rod is simplified into a cantilever beam structure. The static model of the vibration reduction grinding rod considering the damping coefficient is established, which can be expressed as

[0067]

[0068] (ρA) equiv =ρ1A1+ρ2A2+ρ3A3 (2)

[0069] in, is the equivalent density of the vibration reduction grinding rod cross section, ρ i A i Is the product of the density and area of ​​the i-th layer. (EI) equiv is the equivalent bending modulus of the vibration-damping grinding rod, η is the damping ratio coefficient of the overall structure of the vibration-damping grinding rod, (EI) equiv is the equivalent bending stiffness of the vibration damping rod, which is equal to the sum of the bending stiffness of the damping core, carbon fiber layer and metal shell layer, (ρA) equiv Equivalent to ρ equiv , z represents the displacement in the z direction, y is the distance between the analysis point and the end of the grinding rod, and t is the time.

[0070] The static stiffness k of the grinding rod can be expressed as formula (3):

[0071]

[0072] Where j is the number of units in the composite grinding rod, and L is the length of the composite grinding rod.

[0073] According to the uncoupled differential motion equations and the resultant force, the displacement can be expressed as formula (4):

[0074]

[0075] in, Indicates the grinding rod vibration phase angle, q n(t) represents displacement, f n represents the net force, ω represents the angular velocity, ω n Indicates the natural frequency.

[0076] According to formula (4), the response amplitude of the vibration-damping grinding rod is mainly affected by the stiffness and damping ratio of the vibration-damping grinding rod. As the stiffness of the vibration-damping grinding rod material increases, the steady-state response amplitude in each frequency band can be effectively reduced. As the damping ratio increases, the attenuation of the steady-state vibration response can be accelerated, thereby improving the stability of the grinding process.

[0077] S4. Perform static, modal and harmonic response simulation analysis on the radius of the damping core layer and the thickness of the outer shell respectively through finite element analysis software, and establish a mathematical model of the radius of the damping core layer and the thickness of the outer shell based on the analysis data.

[0078] In order to further explore the structural parameters that affect the stiffness and damping ratio of the vibration reduction grinding rod, such as Figure 6 The figure shows the cross-sectional structure of a large aspect ratio vibration-damping grinding rod, where T1 is the radius of the damping core layer, T2 is the thickness of the carbon fiber layer, and T3 is the thickness of the metal shell layer. When the vibration-damping grinding rod vibrates, the vibration of the vibration-damping grinding rod can be simplified to the pure bending vibration of the beam element, so the resultant force in the z direction is zero. The system stress of the three-layer cantilever beam structure can be expressed as formula (5):

[0079]

[0080] Among them, E1, E2 and E3 are the elastic moduli of the three-layer structural materials respectively, and Δ represents the distance between the neutral plane of the vibration-damping grinding rod (the plane with zero stress) and the interface between the carbon fiber and the damping carbon fiber, which can be expressed as formula (5):

[0081]

[0082] Therefore, the bending stiffness of the vibration-damping grinding rod can be obtained, which is expressed as formula (7):

[0083]

[0084] The structural damping coefficient can be expressed as formula (8):

[0085]

[0086] Where β is the elastic modulus coefficient.

[0087] Among them, A, B, C, and D can be expressed as formula (9):

[0088]

[0089] Based on the above formula, we can determine the impact of carbon fiber thickness and damping core thickness on the overall dynamic performance of the grinding rod. Increasing the damping core thickness increases the rod's structural damping coefficient, but because the elastic modulus of the viscoelastic damping material is much smaller than that of the carbon fiber, the rod's overall static stiffness decreases. Increasing the carbon fiber thickness significantly improves the rod's overall stiffness, but decreases the damping coefficient and structural damping capacity. Therefore, optimizing the rod's damping core radius and carbon fiber thickness is crucial.

[0090] Eight values ​​of the damping core diameter, ranging from 0 to 4 mm, were selected for single-factor analysis. The initial outer shell thickness of the vibration-damping grinding rod was set at 1 mm. Static, modal, and harmonic response analyses were performed on the vibration-damping grinding rod structures with different damping core diameters. The results are shown in Table 3. The damping core diameter has little effect on the static stiffness of the vibration-damping grinding rod, with the normal deflection varying within a range of 4 ± 0.2 μm. This is primarily due to the damping core being the innermost layer of the vibration-damping grinding rod, and the static stiffness of the vibration-damping grinding rod is primarily influenced by the elastic modulus of the outer layer material. The first-order natural frequency of the vibration-damping grinding rod decreases with increasing damping core diameter, with the variation around 50 Hz, representing 5%. The dynamic deformation is minimized when the damping core diameter is 3 mm. The following conclusion can be drawn: Due to the low elastic modulus of viscoelastic materials, increasing the diameter of the damping core layer will reduce the static stiffness and natural frequency to a certain extent. However, it will also increase the damping effect to a certain extent, dissipating the energy in the vibration, thereby reducing the amplitude and improving the dynamic stiffness of the vibration-damping grinding rod. Taking all factors into consideration, since the vibration-damping grinding rod primarily requires high dynamic stiffness, a damping core diameter of 3mm is determined to be the optimal size parameter.

[0091] Table 3 Effect of the radius of the damping core layer on the performance parameters of the vibration-damping grinding rod

[0092]

[0093]

[0094] Another structural parameter of a large aspect ratio vibration-damping grinding rod is the thickness of its metal shell. Six groups of grinding rods with different wall thicknesses were selected for static, modal, and harmonic response simulation analysis. The effect of shell thickness on the performance parameters of the grinding rod is shown in Table 4. As the rod shell thickness increases, the maximum deformation of the grinding rod increases, and the static stiffness decreases. This is because the elastic modulus of 40Cr is smaller than that of carbon fiber, and decreasing the thickness of carbon fiber leads to a decrease in static stiffness. The first-order natural frequency of the grinding rod decreases with increasing metal shell thickness because the specific stiffness (E / ρ) of carbon fiber is much greater than that of ordinary steel. The dynamic stiffness of the grinding rod decreases with increasing shell thickness. Taking into account the processing difficulty and application requirements, a shell thickness of 1 mm was selected as the final size.

[0095] Table 4 Effect of shell thickness on performance parameters of vibration damping grinding rod

[0096]

[0097] S4. Optimizing the structural parameters of the three-dimensional structural model, establishing mathematical models of the radius of the damping core layer, the thickness of the metal shell, and the fillet, and optimizing the vibration-damping grinding rod according to the mathematical models.

[0098] The final structural parameter of a high-aspect-ratio vibration-damping grinding rod is the fillet. To address stress concentration within the grinding rod, fillet design is necessary. Table 5 shows the effects of fillet radii ranging from 0 to 2.5 mm on static, modal, and harmonic responses, based on the structure of the vibration-damping grinding rod. Increasing the fillet radius reduces the maximum static deformation by 0.08 μm and increases the static stiffness by 2%. The maximum dynamic deformation increases by 0.11 μm, and the dynamic stiffness increases by 3.1%. The first-order natural frequency increases with increasing fillet radius, while the maximum stress decreases by 0.24 MPa, or approximately 14%. This effectively addresses stress concentration at the sudden change in radius of the vibration-damping grinding rod. However, when the fillet radius reaches a maximum of 2.5 mm, both static and dynamic stiffness decrease due to interference between the fillet and the mounting countersunk hole, resulting in reduced performance. Therefore, a fillet radius of 2 mm was selected based on comprehensive considerations.

[0099] Table 5 Effect of fillet on performance parameters of vibration reduction grinding rod

[0100]

[0101]

[0102] S5. According to the established mathematical model, and combined with the static stiffness, natural frequency, dynamic stiffness and maximum stress, the optimized vibration reduction grinding rod is obtained, such as Figure 7 shown.

[0103] In order to verify the optimization results of the large aspect ratio vibration damping grinding rod, the traditional all-steel grinding rod, the composite grinding rod before optimization and the optimized composite grinding rod were subjected to static analysis, modal analysis and harmonic response comparative analysis. The comparison of the static and dynamic maximum deformations is shown in Figures 8(a)-(c) and 9(a)-(c). In the static analysis, the maximum deformation of the optimized grinding rod provided by the present invention was reduced by 0.56μm and the static stiffness was increased by 15% compared with the grinding rod before optimization; compared with the all-steel grinding rod, the maximum deformation was reduced by 1.76μm and the static stiffness was increased by 37%. In the modal analysis, the first-order natural frequency of the optimized grinding rod was increased by 3% compared with the grinding rod before optimization; compared with the all-steel grinding rod, the first-order natural frequency was increased by 20%. In the harmonic response analysis of a 300Hz sinusoidal load, the optimized grinding rod reduced its maximum deformation by 0.35μm, increased its dynamic stiffness by 9.2%, and reduced its maximum stress by 17.8% compared to the unoptimized grinding rod. Compared to the all-steel grinding rod, the maximum deformation was reduced by 1.85μm, the dynamic stiffness was increased by 37.2%, and the maximum stress was reduced by 34.6%.

[0104] The embodiment of the present invention also provides a vibration-damping grinding rod, such as Figure 7As shown, it includes a metal outer shell layer, an adhesive layer, a carbon fiber layer, and a damping core layer sequentially arranged in the metal outer shell layer, and the vibration-damping grinding rod is a cantilever beam structure; the adhesive layer is used to bond the metal outer shell layer and the carbon fiber layer; the carbon fiber layer serves as the rod body of the vibration-damping grinding rod; and the damping core layer is used to increase the damping capacity of the vibration-damping grinding rod, accelerate the amplitude attenuation rate of the grinding rod, and thus reduce the vibration amplitude of the grinding rod. The material of the metal outer shell layer is chromium, and the material of the carbon fiber layer is type A carbon fiber. The dimensions of the vibration-damping grinding rod are a diameter of 14 mm and a length of 120 mm. The diameter of the damping core layer is 3 mm, the fillet is 2 mm, and the outer shell thickness is 1.5 mm. The vibration-damping grinding rod provided in the embodiment of the present invention can realize the internal grinding of deep holes with a large aspect ratio. The combined action of the carbon fiber layer, the damping core layer, and the adhesive layer changes the natural frequency, damping ratio, and stiffness of the grinding system, thereby improving the stability of the grinding process.

[0105] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0106] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0107] The above specific embodiments of the present invention do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A design optimization method for a vibration-damping grinding rod, characterized in that: The following steps are involved: S1. Constructing a three-dimensional structural model of the vibration-damping grinding rod, wherein the three-dimensional structural model at least includes a damping core layer, a carbon fiber layer, and a metal outer shell layer of the vibration-damping grinding rod; S2. Performing static, modal and harmonic response simulation analysis on the three-dimensional structural model using finite element analysis software to obtain data on static stiffness, natural frequency, dynamic stiffness and maximum stress of the vibration-damping grinding rod with different shell materials; S3. Optimizing the three-dimensional structural model using static parameters to obtain the static stiffness and damping ratio of the three-dimensional structural model, and establishing a static model related to the static stiffness and damping ratio; S4, optimizing the structural parameters of the three-dimensional structural model, establishing a mathematical model of the radius of the damping core layer and a mathematical model of the thickness of the metal shell, and optimizing the vibration-damping grinding rod according to the mathematical models; S5. Based on the established mathematical model and in combination with the static stiffness, natural frequency, dynamic stiffness and maximum stress, a vibration-damping grinding rod with optimized design is obtained; The statics model in step S3 is shown in formula (1) to formula (3): （1） （2） Where, is the equivalent density of the vibration-damping grinding rod cross section, is the product of the density and area of ​​the i-th layer of material, It is the force applied externally to the vibration-damping grinding rod during the grinding process. is the damping ratio coefficient of the overall structure of the vibration-damping grinding rod, is the equivalent bending stiffness of the vibration damping grinding rod, which is equal to the sum of the bending stiffness of the damping core, carbon fiber layer and metal shell layer; The static stiffness k of the grinding rod is expressed as formula (3): （3） Where, j is the number of units in the composite grinding rod, and L is the length of the composite grinding rod; The mathematical model of the structural damping ratio coefficient based on the radius of the damping core layer and the thickness of the metal shell layer in step S4 is shown in formula (4) and formula (5): （4） （5） Where, is the radius of the damping core, is the thickness of the carbon fiber layer, is the thickness of the outer shell, 、 and They are the elastic modulus of the three-layer structural materials: the damping core layer, the carbon fiber layer, and the metal shell layer.

2. The design optimization method of the vibration-damping grinding rod according to claim 1 is characterized in that: The step S2 is specifically as follows: S201, establish a finite element model, define model material parameters, apply loads and boundary conditions, and divide the mesh; S202, performing static, modal and harmonic response simulation analysis on the three-dimensional structural model using finite element analysis software; S203. Obtain data on static stiffness, natural frequency, dynamic stiffness, and maximum stress of vibration-damping grinding rods with different shell materials.

3. The design optimization method of the vibration-damping grinding rod according to claim 2, characterized in that: In the step S201, During the process of applying load and constraint, a fixed constraint is applied to the clamping part of the left end face of the vibration-damping grinding rod, and a grinding force is applied at any point on the tip of the grinding wheel.

4. A vibration-damping grinding rod implemented by the design optimization method according to any one of claims 1 to 3, comprising a metal outer shell layer, characterized in that: It also includes an adhesive layer, a carbon fiber layer, and a damping core layer which are sequentially arranged in the metal outer shell layer, and the vibration-damping grinding rod is a cantilever beam structure.

5. The vibration-damping grinding rod according to claim 4, characterized in that: The material of the metal outer shell layer is chromium.

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