Ultrasonic-assisted grinding metal surface topography and roughness prediction method considering amplitude change under loading state

Abstract

The present invention discloses a method for predicting the surface topography and roughness of ultrasonic-assisted grinding of metals considering the amplitude change under the loading state. The specific steps are as follows: S1. Establish a grinding wheel end face model considering the random distribution of abrasive grains according to the grinding wheel grit size and dimensions, obtain the three-dimensional grinding trajectories of the abrasive grains in the axial ultrasonic-assisted end face grinding, generate the processed surface three-dimensional data matrix and calculate the surface roughness value. S2. Calculate the surface roughness of the axial ultrasonic-assisted end face grinding at different amplitudes to obtain the variation function of the roughness with the amplitude. S3. Conduct a pre-experiment on the ultrasonic vibration-assisted end face grinding and measure the roughness value actually. S4. Determine the ultrasonic amplitude under the actual loading condition based on the variation function. Substitute the calculated actual amplitude into the model constructed in S1, calculate the surface topography simulation and roughness value of the ultrasonic-assisted end face grinding of metals, and verify the prediction result.

Description

Technical Field

[0001] The present invention relates to the field of axial ultrasonic-assisted face grinding, and particularly to a method for predicting the surface topography and roughness of ultrasonic-assisted grinding of metals considering the amplitude change under the loading state. Background Technique

[0002] Ultrasonic-assisted grinding refers to a composite machining method in which ultrasonic vibration is applied to a tool or a workpiece on the basis of traditional grinding to achieve material removal. Compared with traditional grinding machining, ultrasonic-assisted grinding can reduce the grinding force, improve the material removal rate, relieve the wheel clogging, and extend the wheel life. Currently, it has become one of the effective methods to solve the machining problems of difficult-to-machine materials.

[0003] According to the different directions of vibration, ultrasonic-assisted grinding can be divided into axial ultrasonic-assisted grinding, radial ultrasonic-assisted grinding, elliptical ultrasonic-assisted grinding, etc. Among them, the direction of ultrasonic vibration in axial ultrasonic-assisted grinding is the same as the axial direction of the grinding wheel. Since its implementation and control are relatively simple and the improvement effect of machining quality is obvious, it has been widely used at present. Axial ultrasonic-assisted grinding can be further divided into axial ultrasonic-assisted peripheral grinding and axial ultrasonic-assisted face grinding according to different grinding methods. Axial ultrasonic-assisted face grinding uses the end face of the grinding wheel for grinding. At this time, the direction of ultrasonic vibration is the same as the direction of the cutting depth. It can not only reduce the axial grinding force and tool wear, but also increase the residual compressive stress on the machined surface by the ultrasonic frequency knocking of the grinding wheel on the workpiece surface, and improve the service life of the workpiece. Axial ultrasonic-assisted face grinding is widely used in the machining of difficult-to-machine materials, and the surface roughness after grinding has an important impact on the service performance such as friction and fatigue of components.

[0004] The surface micro-topography and roughness have an important influence on the tribological properties, fatigue life and other service performances of components, and are one of the important factors reflecting the grinding quality. Effective prediction of the surface micro-topography and roughness is the basis for further controlling and optimizing the grinding process. At present, the prediction models can be mainly divided into three categories: empirical models, finite element simulation models and theoretical models. The empirical model is obtained by summarizing a large amount of experimental data. It is simple to operate and accurate in prediction, but requires a large number of experiments and has poor model portability. The finite element model refers to simulating the tool shape, trajectory and the interaction with the workpiece through finite element simulation software, and then simulating the machined surface and obtaining its topography and roughness. This method has a simple process and requires less experimental volume, but in order to increase the model accuracy, it is necessary to reduce the size of the material surface grid unit, increasing the calculation amount. The theoretical model is a mathematical description of the machining process. Although the modeling process is somewhat difficult, it requires few experiments. Compared with the finite element model, the operation time is greatly shortened, and the process variables can be analyzed and studied. At present, HF.C. et al. have established a theoretical prediction model for the metal surface topography and roughness of axial ultrasonic assisted peripheral grinding. The predicted surface topography is in good agreement with the measurement results, but there is still a gap between the predicted roughness value and the measurement results. During the ultrasonic assisted grinding process, the amplitude is a very important processing parameter, and its magnitude has a great influence on both the grinding surface topography and roughness. In the actual research process, the ultrasonic amplitude is generally measured by a laser displacement sensor and other methods under no-load conditions, while the actual amplitude during the machining process is very difficult to measure. Research shows that under the action of an external load, the ultrasonic vibration will be inhibited to a certain extent, resulting in a decrease in amplitude. For axial ultrasonic assisted face grinding, due to the large axial load borne by the grinding wheel during the machining process, its amplitude attenuation phenomenon needs to be particularly concerned. However, in the current theoretical prediction models of ultrasonic assisted grinding surface micro-topography and roughness, the amplitude attenuation phenomenon during the machining process has not been considered. And for axial ultrasonic vibration assisted face grinding, there is no published theoretical model for predicting its surface micro-topography and roughness. Summary of the Invention

[0005] Based on the study of the influence law of amplitude on surface roughness, the present invention proposes the concept of amplitude attenuation coefficient and applies it to the theoretical prediction model of the metal surface topography and roughness of axial ultrasonic vibration assisted face grinding, realizing the effective prediction of the surface topography and roughness. The technical means adopted by the present invention are as follows:

[0006] A method for predicting the metal surface topography and roughness of ultrasonic assisted grinding considering the amplitude change under the loading state, comprising the following steps:

[0007] S1. Establish a grinding wheel end face model considering the random distribution of abrasive grains according to the grinding wheel grain size and dimensions, obtain the three-dimensional grinding trajectories of abrasive grains in axial ultrasonic-assisted end face grinding, generate the three-dimensional data matrix of the machined surface, and calculate the surface roughness value.

[0008] S2. Calculate the surface roughness of axial ultrasonic-assisted end face grinding at different amplitudes, and obtain the variation function of roughness with amplitude.

[0009] S3. Conduct a pre-experiment on ultrasonic vibration-assisted end face grinding and measure the roughness value.

[0010] S4. Determine the ultrasonic amplitude of the actual loading condition based on the variation function. Substitute the calculated actual amplitude into the model constructed in S1, calculate the surface topography simulation and roughness value of metal ultrasonic-assisted end face grinding, and verify the prediction results.

[0011] The specific steps of step S1 are as follows:

[0012] S11. Grinding wheel modeling. For any two abrasive grains Ga,b,c and Gl,m,n, the following formula is satisfied:

[0013]

[0014] In the formula and are the diameters of the two abrasive grains respectively;

[0015] S12. Modeling of the cutting trajectory of the abrasive grain center considering the actual depth of cut: Establish a grinding wheel coordinate system with the center of the bottom surface of the grinding wheel as the origin, the workpiece feed direction as the x direction, and the axial direction of the grinding wheel as the z direction. Only during end face grinding, the initial phase angle and the angle ωt of the grinding wheel rotation are in the same plane. Then, the motion trajectory of the center of a single abrasive grain in the grinding wheel coordinate system can be expressed as:

[0016] where the workpiece feed speed is v f , the ultrasonic vibration frequency is f, the amplitude is A, represents the distance from the center of the abrasive grain ball to the center of the grinding wheel, and x G , y G , z G represent the coordinate values of the center of the abrasive grain ball in the grinding wheel coordinate system respectively; t represents the machining time;

[0017] For any abrasive grain G, its initial actual depth of cut is expressed as:

[0018] where a p represents the given depth of cut,

[0019] where r G respectively represent the z - value of the central position coordinate of the abrasive grain G and the radius of the abrasive grain; r α respectively represent the abrasive grain G a the z - value of the central position coordinate and the abrasive grain radius. Due to the action of axial ultrasonic vibration, the actual cutting depth a of the abrasive grain s changes with time, and its change law is expressed as:

[0020]

[0021] S13. Three - dimensional cutting trajectory modeling of axial ultrasonic - assisted face grinding. Taking the center of the abrasive grain as the origin coordinate OG, the cutting speed direction at the position where the center of the abrasive grain is located as the yG direction, and the axial direction of the grinding wheel as the zG direction to establish the abrasive grain coordinate system. Let the angle of any point on the arc relative to the coordinate origin of the grinding wheel be α, and the angle between the vertex of the arc participating in cutting and the coordinate origin be β. Then the cutting trajectory of the abrasive grain in the abrasive grain coordinate system can be expressed as:

[0022]

[0023] By coordinate conversion, the equations of the plowing areas on the right and left sides of the abrasive grain are calculated respectively as:

[0024]

[0025]

[0026] In the formula, Vx2 = r G sinβ + a.

[0027] S14. Roughness calculation. Select the area on the workpiece surface as the analysis domain, and perform grid division on this area according to a certain density. Substitute the relevant parameters of the abrasive grains passing through the analysis domain and the time nodes into the cutting trajectory equation to generate a trajectory scatter point coordinate matrix with a certain density; map the trajectory scatter points to the grid nodes of the analysis domain, and only retain the lowest point coordinate value and store it in the analysis domain coordinate matrix; perform three - dimensional Gaussian noise reduction processing on the result matrix to eliminate unreasonable data and obtain the surface micro - topography and roughness data.

[0028] In step S2, based on the method described in S1, obtaining the variation function of roughness with amplitude has the following steps:

[0029] S21. Use the constructed model to calculate the surface roughness of axial ultrasonic - assisted face grinding at different amplitudes, and draw the curve graph of the theoretical calculated value of the surface roughness Ra at different amplitudes;

[0030] S22. Calibrate the influence index n of amplitude on roughness by the method of drawing the surface roughness Ra at different amplitudes;

[0031] S23. Calculate the theoretical roughness Ra under no-load amplitude using the constructed model;

[0032] S24. Select at least one set of parameters for pre-grinding tests, measure the ultrasonic amplitude A under no-load conditions and the actual surface roughness Ra0 of the workpiece after machining;

[0033] S25. Calculate the axial ultrasonic-assisted face grinding amplitude attenuation coefficient KA according to the following formula. KA is the ratio of the amplitude A0 under the actual loading state to the amplitude A measured under no-load;

[0034]

[0035] Furthermore, in step S3, for the ultrasonic vibration-assisted face grinding pre-experiment and the actual measurement of the roughness value, the following steps are included:

[0036] S31. Under the conditions of spindle speed n = 2000 rpm, feed rate vf = 60 mm / min, and depth of cut ap = 40 μm, obtain the comparison diagram of the measured surface topography and the simulated topography of ordinary face grinding and axial ultrasonic-assisted face grinding (A = 4 μm).

[0037] In step S4, to determine the ultrasonic amplitude under the actual loading condition based on the variation function, the following steps are included:

[0038] S41. Select different grinding parameters for grinding tests, and measure the surface topography and roughness after machining.

[0039] S42. During ordinary grinding, the abrasive grains perform a two-dimensional spiral feed motion, and the grooves are parallel to each other; during ultrasonic-assisted grinding, the abrasive grains are superimposed with a sinusoidal ultrasonic motion while rotating. The trace marks of the sinusoidal motion interfere with the parallel grooves, resulting in reticular stripes.

[0040] S43. Through comparative analysis, it can be found that whether it is the groove texture of ordinary grinding or the reticular texture of axial ultrasonic-assisted face grinding, the predicted surface micro-topography features using the model in this paper are basically consistent with the measurement results.

[0041] S44. By plotting the comparison curve of the measured and predicted roughness values of axial ultrasonic-assisted face grinding (A0 = 4 μm) under different grinding parameters, the average deviation of the predicted value relative to the measured value is 5.33%. The experimental verification results show that the predicted value can accurately reflect the surface roughness values under different process parameters. Description of the Drawings

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] Figure 1 Axial ultrasonic-assisted grinding test platform diagram in the specific embodiment of the present invention;

[0044] Figure 2 Schematic diagram of the end face grinding wheel morphology and abrasive grain distribution in the specific embodiment of the present invention;

[0045] Figure 3 Schematic diagram of ultrasonic-assisted end face grinding and grinding wheel coordinate system in the specific embodiment of the present invention;

[0046] Figure 4 Schematic diagram of the actual depth of cut in the abrasive grain coordinate system in the specific embodiment of the present invention;

[0047] Figure 5 Schematic diagram of the relationship between the grinding wheel coordinate system and the abrasive grain coordinate system in the specific embodiment of the present invention;

[0048] Figure 6 Schematic diagram of the analysis domain setting in the surface topography generation algorithm in the specific embodiment of the present invention;

[0049] Figure 7 Flow chart of grinding surface topography and roughness prediction in the specific embodiment of the present invention;

[0050] Figure 8 Surface roughness R under different spindle speeds in the specific embodiment of the present invention a Comparison diagram of predicted values and experimental values;

[0051] Figure 9 Schematic diagram of the theoretical calculated values of surface roughness Ra under different amplitudes in the specific embodiment of the present invention;

[0052] Figure 10 Measurement diagram of the surface topography of ordinary end face grinding in the specific embodiment of the present invention;

[0053] Figure 11 Prediction diagram of the surface topography of ordinary end face grinding in the specific embodiment of the present invention;

[0054] Figure 12 Measurement diagram of ultrasonic-assisted end face grinding in the specific embodiment of the present invention;

[0055] Figure 13 Prediction diagram of ultrasonic-assisted end face grinding in the specific embodiment of the present invention;

[0056] Figure 14Comparison diagram of measured and predicted values of surface roughness Ra at different feed rates in the specific embodiments of the present invention;

[0057] Figure 15 Comparison diagram of measured and predicted values of surface roughness Ra at different grinding depths in the specific embodiments of the present invention. Specific embodiments

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0059] The present invention discloses a method for predicting the surface topography and roughness of metal during ultrasonic-assisted grinding considering the amplitude change under the loading state. Please refer to Figure 1 , in order to verify the surface topography and roughness prediction model for axial ultrasonic-assisted face grinding, an ultrasonic vibration system developed independently was used to build an axial ultrasonic-assisted grinding test platform on a three-axis vertical milling machine for axial ultrasonic-assisted face grinding tests. The ultrasonic vibration system uses a contact transmission method, with an ultrasonic system vibration frequency of 28.2 kHz and an amplitude of 4 μm under no-load conditions. The three-axis vertical milling machine selects the NHX8000 machine tool of Beijing Ninghua Co., Ltd., with a maximum rotational speed of up to 18,000 r / min, a spindle power of 5.5 kW, and a positioning accuracy of up to 0.003 mm. The no-load amplitude measuring device selects the LK-H025 type laser displacement sensor, with a maximum sampling frequency of 400 kHz, a measuring range of 3 mm, and a repeatability accuracy of 0.02 μm. The surface topography and roughness after grinding are obtained by measuring with a 3D surface optical profiler (ZYGO 2020AA7B). The roughness at each parameter is measured 3 times repeatedly. The grinding wheel selects a CBN ceramic bond grinding wheel, with a diameter of 16 mm, a grit size of 80#, and a concentration of 100%. The topography of the grinding wheel is obtained by an INSIZE (ISM-DL) optical microscope, and the abrasive grain size and abrasive grain spacing (offset) are measured at randomly selected positions on the grinding wheel surface, with 50 repeated measurements. The ultrasonic vibration assistance frequency is 26.5 kHz, the cooling method is oil cooling, and the grinding workpiece material is nickel-based superalloy GH4169.

[0060] Based on the study of the influence law of amplitude on surface roughness, the present invention proposes the concept of amplitude attenuation coefficient and applies it to the theoretical model for predicting the surface topography and roughness of metal during axial ultrasonic vibration-assisted face grinding, realizing the effective prediction of surface topography and roughness, which has theoretical significance and engineering value.

[0061] Specifically, the method has the following steps:

[0062] S1. The method of HF.C. et al. is adopted to model the grinding wheel. The end face of the grinding wheel used in the experiment is modeled through the MATLAB numerical simulation software. The established end face model of the grinding wheel is as Figure 2 shown; the specific modeling process is as follows:

[0063] Grinding wheel modeling: Considering that there cannot be physical overlap between abrasive grains, that is, the distance between the centers of two abrasive grains should be greater than the sum of the radii of these two abrasive grains. Therefore, for any two abrasive grains G a,b,c and G l,m,n the following formula needs to be satisfied, where and are the diameters of the two abrasive grains respectively.

[0064]

[0065] S12. Modeling of the cutting trajectory of the abrasive grain center considering the actual depth of cut. Taking the center of the bottom surface of the grinding wheel as the origin, the workpiece feed direction as the x-direction, and the axial direction of the grinding wheel as the z-direction to establish the grinding wheel coordinate system. Only during surface grinding, the initial phase angle of the abrasive grain and the angle ωt of the grinding wheel rotation are in the same plane. Then, the motion trajectory of the center of a single abrasive grain in the grinding wheel coordinate system can be expressed as:

[0066]

[0067] For any abrasive grain G, its initial actual depth of cut can be expressed as:

[0068]

[0069] where r G respectively represent the z value of the center position coordinate of the abrasive grain G and the radius of this abrasive grain; rα respectively represent the z value of the center position coordinate of the abrasive grain G a and the radius of the abrasive grain. Due to the action of axial ultrasonic vibration, the actual depth of cut a s of the abrasive grain changes with time, and its change law can be expressed as:

[0070]

[0071] S13. Modeling of the three-dimensional cutting trajectory of axial ultrasonic-assisted surface grinding. Taking the center of the abrasive grain as the origin coordinate OG, the cutting speed direction at the position where the center of the abrasive grain is located as the yG direction, and the axial direction of the grinding wheel as the zG direction to establish the abrasive grain coordinate system. Let the angle of any point on the arc relative to the origin of the grinding wheel coordinate be α, and the angle between the vertex of the arc participating in cutting and the origin of the coordinate be β. Then, the cutting trajectory of the abrasive grain in the abrasive grain coordinate system can be expressed as:

[0072]

[0073] The equations of the plowing areas on the right and left sides of the abrasive grains are obtained through coordinate conversion as follows:

[0074]

[0075]

[0076] where Vx2 = r G sinβ + a.

[0077] S14. Roughness calculation: The area on the workpiece surface is defined as the analysis domain, and the area is meshed according to a certain density. The relevant parameters of the abrasive grains passing through the analysis domain and the time nodes are substituted into the cutting trajectory equation to generate a trajectory scatter point coordinate matrix with a certain density; the trajectory scatter points are mapped to the grid nodes of the analysis domain, and only the lowest point coordinate values are stored in the analysis domain coordinate matrix; the result matrix is subjected to three-dimensional Gaussian noise reduction processing to eliminate unreasonable data such as spikes, and the surface microtopography and roughness data are obtained.

[0078] Specifically, as Figure 3 shown, the motion relationship of axial ultrasonic assisted face grinding can be regarded as the superposition of the rotational motion of the grinding wheel, the axial ultrasonic vibration, and the workpiece feed motion, where the workpiece feed speed is v f , the grinding wheel linear speed is v s , the ultrasonic vibration frequency is f, and the amplitude is A; the rotational angular velocity of the grinding wheel is ω, and any abrasive grain is G; a grinding wheel coordinate system is established with the center of the bottom surface of the grinding wheel as the origin, the workpiece feed direction as the x direction, and the axial direction of the grinding wheel as the z direction. Only during face grinding, the initial phase angle of the abrasive grain and the angle ωt of the grinding wheel rotation are in the same plane, then the motion trajectory of the center of a single abrasive grain in the grinding wheel coordinate system can be expressed as:

[0079]

[0080] As Figure 4 shown, G a represents the abrasive grain at the lowest point of the grinding wheel end face. Due to the random distribution characteristics of the abrasive grains and the normal distribution characteristics of the abrasive grain size, when grinding the workpiece with a given cutting depth a p , except for the abrasive grain at the lowest point, the initial cutting depths of other abrasive grains do not reach a p ; therefore, for any abrasive grain G, its initial actual cutting depth can be expressed as:

[0081]

[0082] where r G respectively represent the z-value of the central position coordinate of the abrasive grain G and the radius of the abrasive grain; r α respectively represent the z-value of the central position coordinate of the abrasive grain Ga and the abrasive grain radius. Due to the action of the axial ultrasonic vibration, the actual cutting depth a of the abrasive grain s changes with time, and its change law can be expressed as:

[0083]

[0084] In the actual grinding process, the normal direction of the actual grinding section of the abrasive grain is consistent with the velocity direction, that is, consistent with the tangent direction of the trajectory. In order to represent the cutting section of the abrasive grain in the grinding wheel coordinate system to obtain the cutting motion trajectory of the grinding wheel, coordinate transformation is required. As Figure 5 (a) shows, the rotation angle of the abrasive grain coordinate system relative to the grinding wheel coordinate system is -γ; as Figure 5 (a) shows, with the center of the abrasive grain as the origin coordinate O G , the cutting velocity direction at the position where the center of the abrasive grain is located is the y G direction, and the axial direction of the grinding wheel is the z G direction to establish the abrasive grain coordinate system. The relationship between the grinding wheel coordinate system and the abrasive grain coordinate system is as Figure 5 (a) shows. As Figure 5 (b) shows, in the actual grinding process, in the x G O G z G plane, only part of the arc of the abrasive grain participates in cutting. The shaded area in the figure is the actual grinding section of the abrasive grain. The angle of any point on the arc relative to the origin of the grinding wheel coordinates is set as α, and the angle between the vertex of the arc participating in cutting and the origin of coordinates is set as β. Then the cutting trajectory of the abrasive grain in the abrasive grain coordinate system can be expressed as:

[0085]

[0086] where α ∈ (-β, β), β = arccos[(r G -α s ) / r G .

[0087] As Figure 6 shown: Select the area on the workpiece surface to be defined as the analysis domain, and perform mesh division on this area according to a certain density. The x-axis range of the analysis domain is [x min , x max , the y-axis range is [y min , y max , and then assign an initial z-value to each grid point in this area. The grinding wheel center has no movement in the y direction. Therefore, as Figure 6As shown, for any abrasive grain G within each rotation axis, the entry phase and the exit phase entering the analysis domain are fixed and unchanging. According to geometric relationships, it can be obtained that:

[0088]

[0089] The prediction process of the surface topography and roughness of axial ultrasonic assisted face grinding is as Figure 7 shown.

[0090] Axial ultrasonic assisted face grinding (A = 4μm) and ordinary face grinding tests (A = 0μm) were respectively carried out using the test conditions described above. The grinding feed speed v f = 40mm / min, the depth of cut a p = 20μm, the rotational speed n = 1000rpm, 2000rpm, 3000rpm, 4000rpm. Meanwhile, the roughness was calculated using the above prediction model. The number of abrasive grains on the grinding wheel in the model was set to 3 layers, and the data interval in the analysis domain was set to 1μm. The results are as Figure 8 shown;

[0091] The surface roughness of axial ultrasonic assisted face grinding at different amplitudes was calculated using the model described above, and the calculation results are as Figure 9 shown. It can be found that when the amplitude A changes from 0μm to 6μm, the roughness R a increases with the increase of the amplitude, and the roughness R a basically satisfies the power exponential relationship shown in Equation (a), where B and n are constants related to the test conditions. Equation (a) can be transformed into Equation (b). Therefore, taking lnA as the abscissa and lnR a as the ordinate for least squares fitting can determine the values of n and B, and the fitting results are as Figure 9 shown.

[0092] R a = B·A n (a)

[0093] ln R a = n ln A + ln B (b)

[0094] As Figure 10 shown, it is a comparison diagram of the measured surface topography and the simulated topography of ordinary face grinding and axial ultrasonic assisted face grinding (A = 4μm) with the spindle speed n = 2000rpm, the feed speed v f = 60mm / min, and the depth of cut a p = 40μm; the measurement diagram of the surface topography of ordinary face grinding;

[0095] AsFigure 11 As shown, for the spindle speed n = 2000 rpm, feed rate v f = 60 mm / min, depth of cut a p = 40 μm, comparison diagram of the measured and simulated surface topographies of ordinary surface grinding and axial ultrasonic-assisted surface grinding (A = 4 μm), prediction diagram of the ordinary surface grinding surface topography; in this paper, the end face of the grinding wheel used in the experiment was modeled by the MATLAB numerical simulation software;

[0096] As Figure 12 shown, for the spindle speed n = 2000 rpm, feed rate v f = 60 mm / min, depth of cut a p = 40 μm, comparison diagram of the measured and simulated surface topographies of ordinary surface grinding and axial ultrasonic-assisted surface grinding (A = 4 μm), measurement diagram of the ultrasonic-assisted surface grinding;

[0097] As Figure 13 shown, for the spindle speed n = 2000 rpm, feed rate v f = 60 mm / min, depth of cut a p = 40 μm, comparison diagram of the measured and simulated surface topographies of ordinary surface grinding and axial ultrasonic-assisted surface grinding (A = 4 μm), prediction diagram of the ultrasonic-assisted surface grinding;

[0098] As Figure 14 and Figure 15 shown is the comparison of the roughness measurement values and prediction values of axial ultrasonic-assisted surface grinding (A0 = 4 μm) under different feed rates and grinding depths. It can be found that there is a good consistency between the prediction values and the measurement values, and the average deviation of the prediction values relative to the measurement values is 5.33%.

[0099] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An ultrasonic-assisted grinding metal surface topography and roughness prediction method considering the amplitude change under the loading state, characterized in that It includes the following steps: S1. Establish a grinding wheel end face model considering the random distribution of abrasive grains according to the grinding wheel grit size and dimensions, mathematically describe the three-dimensional grinding trajectories of abrasive grains in axial ultrasonic-assisted end face grinding, generate a three-dimensional data matrix of the machined surface, and calculate the surface roughness value; S2. Calculate the surface roughness of axial ultrasonic-assisted end face grinding at different amplitudes, and obtain the variation function of roughness with amplitude; S3. Conduct a pre-experiment on ultrasonic vibration-assisted end face grinding and measure the roughness value; S4. Determine the ultrasonic amplitude of the actual loading condition based on the variation function, substitute the calculated actual amplitude into the model constructed in S1, calculate the surface topography simulation and roughness value of metal ultrasonic-assisted end face grinding, and verify the prediction result; In step S2, the variation function of roughness with amplitude is obtained based on the method described in S1, and it has the following steps: S21. Calculate the surface roughness of axial ultrasonic-assisted end face grinding at different amplitudes using the constructed model, and draw a curve of the theoretical calculated value of surface roughness Ra at different amplitudes; S22. Calibrate the influence index n of amplitude on roughness by drawing the method of surface roughness Ra at different amplitudes; S23. Calculate the theoretical roughness Ra under no-load amplitude using the constructed model; S24. Select at least one set of parameters for pre-grinding experiments, measure the ultrasonic amplitude A under no-load conditions and the actual surface roughness Ra0 of the workpiece after machining; S25. Calculate the amplitude attenuation coefficient KA of axial ultrasonic-assisted end face grinding according to the following formula. KA is the ratio of the amplitude A0 under the actual loading state to the amplitude A measured under no-load; 2. The ultrasonic-assisted grinding metal surface topography and roughness prediction method considering the amplitude change under the loading state according to claim 1, characterized in that: The specific steps of step S1 include the following steps: S11. Grinding wheel modeling. For any two abrasive grains Ga,b,c and Gl,m,n, the following formula is satisfied: wherein and are the diameters of two abrasive grains, respectively; S12. Modeling of the cutting trajectory of the abrasive grain center considering the actual depth of cut. Taking the center of the bottom surface of the grinding wheel as the origin, the workpiece feed direction as the x-axis, and the axial direction of the grinding wheel as the z-axis to establish the grinding wheel coordinate system. Only during surface grinding, the initial phase angle of the abrasive grain is in the same plane as the rotation angle ωt of the grinding wheel. Then, the motion trajectory of the center of a single abrasive grain in the grinding wheel coordinate system can be expressed as: Among them, the workpiece feed speed is v f , the ultrasonic vibration frequency is f, and the amplitude is A, represents the distance from the center of the abrasive grain sphere to the center of the grinding wheel, and x G , y G , z G respectively represent the coordinate values of the center of the abrasive grain sphere in the grinding wheel coordinate system; t represents the machining time; For any abrasive grain G, its initial actual cutting depth can be expressed as: where a p represents a given cutting depth Among them r G respectively represent the z value of the central position coordinate of the abrasive grain G and the radius of the abrasive grain; r α respectively represent the abrasive grain G a the z value of the central position coordinate and the abrasive grain radius; and due to the action of the axial ultrasonic vibration, the actual cutting depth a of the abrasive grain s changes with time, and its change law can be expressed as: S13. Axial ultrasonic-assisted end face grinding three-dimensional cutting trajectory modeling. Taking the abrasive grain center as the origin coordinate OG, the cutting speed direction at the position of the abrasive grain center as the yG direction, and the grinding wheel axial direction as the zG direction to establish an abrasive grain coordinate system. Let the angle of any point on the arc relative to the grinding wheel coordinate origin be α, and the angle between the vertex of the arc participating in cutting and the coordinate origin be β. Then the cutting trajectory of the abrasive grain in the abrasive grain coordinate system can be expressed as: The plowing area equations on the right and left sides of the abrasive grain are calculated through coordinate conversion respectively: where Vx2 = r G sinβ + a; S14. Roughness calculation. Select the area of the workpiece surface as the analysis domain, and perform grid division on this area according to a certain density. Substitute the relevant parameters and time nodes of the abrasive grains passing through the analysis domain into the cutting trajectory equation to generate a trajectory scatter point coordinate matrix with a certain density; map the trajectory scatter points to the analysis domain grid nodes, and only retain the lowest point coordinate value and store it in the analysis domain coordinate matrix; perform three-dimensional Gaussian noise reduction processing on the result matrix to eliminate unreasonable data and obtain the surface micro-topography and roughness data.

3. The ultrasonic-assisted grinding metal surface topography and roughness prediction method considering the amplitude change under the loading state according to claim 1, characterized in that: In step S3, conduct a pre-experiment on ultrasonic vibration-assisted end face grinding and measure the roughness value, and it has the following steps: S31. Under the conditions of preset spindle speed, feed rate, and depth of cut, obtain the comparison chart of the measured surface topography and the simulated topography of ordinary surface grinding and axial ultrasonic assisted surface grinding.

4. The ultrasonic-assisted grinding metal surface topography and roughness prediction method considering the amplitude change under the loading state according to claim 3, characterized in that: In the step S4, determining the ultrasonic amplitude of the actual loading condition based on the variation function includes the following steps: S41. Select different grinding parameters for grinding tests, and measure the surface topography and roughness after machining; S42. During ordinary grinding, the abrasive grains perform two-dimensional spiral feed motion, and the grooves are parallel to each other; during ultrasonic assisted grinding, the abrasive grains are superimposed with sinusoidal ultrasonic motion while rotating, and the trajectory scratches of the sinusoidal motion interfere with the parallel grooves, resulting in reticular stripes; S43. Plot the comparison curve graph of the measured values and predicted values of the roughness of axial ultrasonic assisted surface grinding under different grinding parameters, and verify the prediction results based on the comparison results.

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