A method for predicting surface geometry and machining precision of ultra-precision cutting

Abstract

The present application belongs to the technical field of ultra-precision machining, and discloses a kind of ultra-precision cutting surface geometric appearance and machining precision prediction method, including obtaining machining parameter, tool parameter and material parameter;According to tool parameter, the cutting edge profile of tool is established, according to machining parameter and material parameter, the profile deformation amount caused by material elastic recovery is calculated, according to machining parameter, tool parameter and material parameter, the profile deformation amount caused by plastic side flow is calculated;Based on the cutting edge profile of tool, the deformation amount caused by material elastic recovery and the deformation amount caused by plastic side flow, the correction coefficient of appearance prediction model under different machining parameters is calculated, and the cutting surface geometric appearance prediction model is obtained;Optimize correction to machining parameter, pre-compensate elastic-plastic deformation amount, and obtain the final cutting surface.The present application considers tool cutting edge profile, elastic recovery and plastic side flow into surface appearance model comprehensively, effectively improves the prediction accuracy of microstructure surface appearance model.

Description

Technical Field

[0001] The present invention relates to the technical field of ultra-precision machining, and in particular to a method for predicting the geometrical appearance and machining accuracy of an ultra-precision cutting surface. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Single-point diamond turning is a cutting technique used to machine high-precision surfaces, capable of directly achieving submicron-level surface topography. Due to the cutting depth of several microns, the impact of microscopic factors such as edge rounding, material elastic recovery, and plastic lateral flow on machining accuracy must be considered.

[0004] Tool profile replication is an important method for diamond turning microstructures. For the predictive modeling of the surface topography of ultra-precision turning microstructures, only the tool profile and cutting trajectory are usually considered. However, due to the influence of material elastic recovery and plastic flow, there is a geometric deviation between the actual surface topography of the workpiece and the tool cutting edge profile. Figure 2 Schematic diagram of the effect of material elastic-plastic deformation on the cross-sectional profile of diamond microgrooves. Currently, there is no definitive elastic-plastic deformation model for diamond cutting microstructures, making it impossible to accurately predict the deformation patterns of the workpiece material affected by cutting forces, tool geometry, and material flow characteristics. This results in a significant deviation between the actual machined surface topography and the designed target. In theoretical models of surface topography for ultra-precision cutting planes, elastic recovery is often attributed to the minimum cutting thickness corresponding to the blunting of the cutting edge, but this theory is not applicable to microstructure machining. Furthermore, theoretical models of plastic lateral flow in the cutting plane are also not applicable to microstructure machining.

[0005] Due to the existence of the above problems, a modeling method that can accurately predict the contour error caused by elastic-plastic deformation is needed to guide the optimization of diamond turning processing parameters and improve its processing accuracy. Summary of the Invention

[0006] In order to solve the above problems, the present invention proposes a method for predicting the geometric morphology and machining accuracy of ultra-precision cutting surfaces, which comprehensively considers the tool cutting edge profile, elastic recovery and plastic lateral flow into the surface morphology model, effectively improving the prediction accuracy of the microstructure surface morphology model.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] In a first aspect, the present invention provides a method for predicting the geometric morphology and machining accuracy of an ultra-precision cutting surface, comprising the following steps:

[0009] obtaining machining parameters, tool geometry parameters, and characteristic parameters of a workpiece to be machined;

[0010] establishing a cutting edge profile of the tool according to the tool geometry parameters, calculating a profile deformation amount caused by material elastic recovery according to the machining parameters and the characteristic parameters of the workpiece to be machined, and calculating a profile deformation amount caused by plastic side flow according to the machining parameters, the tool geometry parameters, and the characteristic parameters of the workpiece to be machined;

[0011] calculating correction coefficients of a topography prediction model under different machining parameters based on the cutting edge profile of the tool, the profile deformation amount caused by material elastic recovery, and the profile deformation amount caused by plastic side flow, and obtaining a cutting surface geometry topography prediction model;

[0012] optimizing and correcting the machining parameters, pre-compensating the elastic-plastic deformation amount, and obtaining a final cutting surface.

[0013] As an optional implementation, the cutting edge profile of the tool is established according to the tool geometry parameters, specifically:

[0014] R t = R ideal + ΔR wave = R ideal + Δw sin(ωθ)

[0015] wherein R ideal is an ideal cutting edge profile of the tool, and Δw is a cutting edge waviness amplitude.

[0016] As an optional implementation, the ideal cutting edge profile of a circular arc-shaped tool with a radius of r can be calculated by the following formula:

[0017]

[0018] The ideal cutting edge profile of a V-shaped pointed tool with a tool tip angle of can be calculated by the following formula:

[0019]

[0020] wherein h is a cutting depth.

[0021] As an optional implementation, the profile deformation amount caused by material elastic recovery includes elastic recovery caused by cutting force and elastic recovery caused by tool edge roundness.

[0022] As an optional implementation, the profile deformation amount caused by plastic side flow includes a micro-groove width reduction caused by plastic side flow and material accumulation at the micro-groove boundary caused by plastic side flow.

[0023] As an optional implementation, the final cutting surface geometry topography prediction model is:

[0024] R model =R t +f d f s f m (e+s+Δh a )

[0025] Among them, f d is the correction factor of the prediction model regarding cutting depth, f s is the correction factor of the prediction model for cutting speed, f m is the correction coefficient of the prediction model for the workpiece material.

[0026] As an optional embodiment, the tool geometric parameters include the arc radius of the arc-shaped tool, the angle of the V-shaped tip, the front angle and the back angle of the tool, and the waviness of the cutting edge profile.

[0027] As an optional embodiment, the characteristic parameters of the workpiece material to be cut include elastic modulus, Poisson's ratio, hardness and yield strength.

[0028] As an optional embodiment, the calculation formula for the material accumulation height at the microgroove boundary caused by plastic lateral flow is:

[0029]

[0030] in, Indicates the equivalent half-apex angle of the diamond tool.

[0031] As an optional embodiment, the calculation formula for the reduction in microgroove width caused by plastic lateral flow is:

[0032] s=k c k m k t h min L t

[0033] Among them, k c is the correction factor, k m is a coefficient determined by the material properties, k t is a coefficient determined by the tool size, L t is the cutting width of the tool.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] This paper proposes a method for predicting the geometric topography and machining accuracy of ultra-precision cutting surfaces. The method studies the influence of material elastic-plastic deformation on the microgroove cross-sectional profile. By incorporating the tool cutting edge profile, elastic recovery, and plastic lateral flow into the surface topography prediction model, the prediction accuracy of the microstructure surface topography model is effectively improved. For metal materials, the average error in the microgroove cross-sectional profile prediction is controlled within 0.08μm, and the maximum error does not exceed 0.30μm. Accurately predicting topography errors before machining and pre-compensating for machining errors by optimizing machining parameters further improves the machining accuracy of ultra-precision cutting.

[0036] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0038] Figure 1 Flowchart of the method for predicting the geometric morphology and machining accuracy of ultra-precision cutting surfaces provided in Example 1 of the present invention;

[0039] Figure 2 Schematic diagram of the effect of elastic-plastic deformation of the material on the cross-sectional profile of diamond microgrooves;

[0040] Figure 3 The tool cutting edge profile measurement results obtained using an optical microscope, where (a) is the measurement result of a circular arc tool with a nominal radius of 100 μm, (b) is the measurement result of a circular arc tool with a nominal radius of 50 μm, and (c) is the measurement result of a V-shaped tip tool with a nominal angle of 140°.

[0041] Figure 4 Schematic diagram of the effect of the elastic recovery component on the cross-sectional profile in the model of the present invention, wherein (a) is the elastic recovery corresponding to the contact pressure of the arc-shaped tool on the workpiece, (b) is the elastic recovery corresponding to the contact pressure of the V-shaped tool on the workpiece, (c) is the elastic recovery corresponding to the bluntness of the arc-shaped tool edge, and (d) is the elastic recovery corresponding to the bluntness of the V-shaped tool edge;

[0042] Figure 5 Schematic diagram of the effect of the plastic lateral flow component on the cross-sectional profile in the model of the present invention, wherein (a) is the plastic lateral flow generated by using a circular arc tool, and (b) is the plastic lateral flow generated by using a V-shaped sharp tool;

[0043] Figure 6 A schematic diagram of selecting a correction coefficient according to different processing parameters in the present invention;

[0044] Figure 7 This is a comparison diagram of the predicted results and experimental results of Example 1 of the ultra-precision turning microstructure surface morphology modeling method of the present invention;

[0045] Figure 8 This is a comparison chart of the predicted results and experimental results of Example 2 of the ultra-precision turning microstructure surface topography modeling method of the present invention;

[0046] Figure 9 This is a comparison chart of the predicted results and experimental results of Example 3 of the ultra-precision turning microstructure surface morphology modeling method of the present invention. DETAILED DESCRIPTION

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0048] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0049] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0050] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0051] Example 1

[0052] like Figure 1 As shown, this embodiment provides a method for predicting the geometric morphology and machining accuracy of an ultra-precision cutting surface, comprising the following steps:

[0053] S1, obtaining machining parameters, tool geometry parameters, and characteristic parameters of the workpiece material to be cut;

[0054] S2. Establishing a cutting edge profile of the tool according to the tool geometric parameters, calculating the profile deformation caused by elastic recovery of the material according to the machining parameters and the characteristic parameters of the workpiece material to be cut, and calculating the profile deformation caused by plastic lateral flow according to the machining parameters, the tool geometric parameters and the characteristic parameters of the workpiece material to be cut;

[0055] S3, based on the tool cutting edge profile, the amount of deformation caused by material elastic recovery and the amount of deformation caused by plastic side flow, calculate the correction coefficient of the topography prediction model under different machining parameters, and obtain a cutting surface geometry topography prediction model;

[0056] S4, optimize and correct the machining parameters, pre-compensate the elastic-plastic deformation, and obtain the final cutting surface.

[0057] Before obtaining the tool geometry parameters, first clean the tool tip of the diamond tool, use a dust-free cotton swab to dip acetone or ethanol to wipe the rake face and the flank face, until no stains and dust can be seen under a total magnification of 500 times, use an optical microscope or a scanning electron microscope to obtain the plan view of the rake face at the tool tip, calculate the tool geometry parameters by digital image processing algorithm, obtain the circular arc radius r of the circular arc tool and the angle of the V-shaped sharp tool Determine the rake angle and the relief angle, use an atomic force microscope to obtain the waviness of the cutting edge profile, and use an optical microscope to obtain the measurement results of the tool cutting edge profile as shown in Figure 3 .

[0058] According to the tool geometry parameters, the cutting edge profile of the tool is established, specifically:

[0059] R t =R ideal +ΔR wave =R ideal +Δwsin(ωθ)

[0060] In the formula, R ideal is the ideal cutting edge profile of the tool, and Δw is the amplitude of the cutting edge waviness.

[0061] Wherein, the ideal cutting edge profile of the circular arc tool with a radius of r can be calculated by the following formula:

[0062]

[0063] The ideal cutting edge profile of the V-shaped sharp tool with a tool tip angle of can be calculated by the following formula:

[0064]

[0065] Wherein, h is the cutting depth.

[0066] Measure the characteristic parameters of the workpiece material, including elastic modulus, Poisson's ratio, hardness, and yield strength. Calculate the contour deformation caused by the material's elastic recovery based on the processing parameters and the characteristic parameters of the workpiece material to be cut. The contour deformation caused by the material's elastic recovery includes the elastic recovery caused by the cutting force and the elastic recovery caused by the blunting of the cutting edge. The schematic diagram of the influence of the elastic recovery component on the cross-sectional profile is shown below. Figure 4 The following formula is used to calculate the contour deformation caused by the elastic recovery of the material:

[0067] e=e1+e2

[0068] Where e1 is the elastic recovery caused by cutting force, and e2 is the elastic recovery caused by cutting edge bluntness.

[0069] The elastic recovery caused by the cutting force corresponding to e1 is simplified into a linear transformation, and its maximum elastic deformation δ is calculated using the following formula:

[0070]

[0071] Where P is the load on the workpiece, E * is the equivalent elastic modulus, and R is the radius of the equivalent sphere.

[0072] The elastic recovery e2 caused by the blunt edge is the same along the microstructure cross-sectional profile. The springback e2 is calculated using the following formula:

[0073] e2=(1-ε p )·h min

[0074] Where h min is the minimum cutting thickness, ε p is the plastic strain.

[0075] According to the stress-strain relationship in the elastic-plastic deformation theory, the plastic strain is calculated σ t is the yield strength of the workpiece, and E is the elastic modulus.

[0076] The contour deformation caused by plastic lateral flow includes the reduction of microgroove width caused by plastic lateral flow and the material accumulation at the microgroove boundary caused by plastic lateral flow.

[0077] According to the machining parameters, tool geometry parameters and characteristic parameters of the workpiece material to be cut, the reduction in microgroove width caused by plastic lateral flow and the accumulation of material at the microgroove boundary are calculated. The schematic diagram of the influence of the plastic lateral flow component on the cross-sectional profile is shown in the figure. Figure 5 The calculation formula for the reduction in microgroove width caused by plastic lateral flow is as follows:

[0078] s=k c k m kt h min L t

[0079] wherein k c is a correction factor, k m is a factor determined by material properties, k t is a factor determined by tool size, L t is the cutting width of the tool.

[0080] The material accumulation height Δh a at the micro-groove boundary is calculated using the following formula:

[0081]

[0082] wherein represents the equivalent half-apex angle of the diamond tool.

[0083] According to the influence of the calculated machining parameters on the micro-groove profile deformation, the cutting depth is pre-compensated before machining, and appropriate machining parameters are selected to reduce the machining surface morphology error caused by elastic-plastic deformation, and finally a higher precision cutting surface is obtained.

[0084] The influence of machining parameters on the elastic-plastic deformation is corrected using correction factors (the correction factors are obtained by experiments, and the specific selection is shown in Figure 6 The cutting depth, cutting speed and workpiece material are calculated according to the following formula:

[0085] R model = R t +f d f s f m (e+s+Δh a )

[0086] wherein f d is the correction factor of the prediction model about the cutting depth, f s is the correction factor of the prediction model about the cutting speed, and f m is the correction factor of the prediction model about the workpiece material. As shown in Figure 6 is a schematic diagram of selecting correction factors according to different machining parameters in the model of the present application.

[0087] The scheme of the present application will be described and verified by specific examples.

[0088] Example 1:

[0089] The micro-groove experiment of ultra-precision turning is carried out to verify the present application. The workpiece material is selected as oxygen-free copper TU2, the machining equipment is selected as a three-axis ultra-precision machining lathe, the tool is selected as a single-point diamond tool with a nominal circular arc of 100 μm, and the micro-groove with a depth of 6 μm is machined on the workpiece at a cutting speed of 5 mm·min-1. The micro-groove cross-sectional profiles of actual machining, the common model and the present model, and the difference between the prediction results of the common model and the present model and the actual machining results are shown in FIG. 1. Figure 7

[0090] Through measurement, the circular arc radius of the tool is 100.95 μm, the rake angle and the relief angle are 0° and 10° respectively, the waviness is 55 nm, the blade blunt circle radius is 50 nm, and the actual cutting depth is 6.76 μm.

[0091] Compared with the prediction results of the common model: the average error of the common model prediction is 0.50 μm, and the maximum error is 1.15 μm; the average error of the present model prediction is 0.06 μm, and the maximum error is 0.25 μm.

[0092] Example 2

[0093] The micro-groove experiment of ultra-precision turning is carried out to verify the present application. The workpiece material is selected as brass H59, the machining equipment is selected as a three-axis ultra-precision machining lathe, the tool is selected as a single-point diamond tool with a nominal circular arc of 50 μm, and the micro-groove with a depth of 6 μm is machined on the workpiece at a cutting speed of 200 mm·min-1. The micro-groove cross-sectional profiles of actual machining, the common model and the present model, and the difference between the prediction results of the common model and the present model and the actual machining results are shown in FIG. 2. Figure 8

[0094] Through measurement, the circular arc radius of the tool is 51.69 μm, the rake angle and the relief angle are 0° and 10° respectively, the waviness is 39 nm, the blade blunt circle radius is 50 nm, and the actual cutting depth is 6.70 μm.

[0095] Compared with the prediction results of the common model: the average error of the common model prediction is 0.16 μm, and the maximum error is 1.08 μm; the average error of the present model prediction is 0.06 μm, and the maximum error is 0.23 μm.

[0096] Example 3

[0097] The micro-groove experiment of ultra-precision turning is carried out to verify the present application. The workpiece material is selected as aluminum alloy 6061, the machining equipment is selected as a three-axis ultra-precision machining lathe, the tool is selected as a single-point diamond tool with a nominal V shape of 140°, and the micro-groove with a depth of 6 μm is machined on the workpiece at a cutting speed of 50 mm·min-1. The micro-groove cross-sectional profiles of actual machining, the common model and the present model, and the difference between the prediction results of the common model and the present model and the actual machining results are shown in FIG. 3.​​Figure 9 The results are shown in the table.

[0098] The measured angle of the tool is 139.92°, the rake angle and the relief angle are 0° and 10° respectively, the waviness is 36 nm, the nose radius is 50 nm, and the actual cutting depth is 7.55 μm.

[0099] Ignoring the influence of the micro-chipping at the tool tip, compared with the prediction results of the common model: the average error of the common model is 0.34 μm, and the maximum error is 0.72 μm; the average error of the prediction of the present model is 0.08 μm, and the maximum error is 0.30 μm.

[0100] The above describes the specific embodiments of the present application in combination with the drawings, but is not a limitation on the protection scope of the present application, and those skilled in the art should understand that various modifications or changes made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the protection scope of the present application.

Claims

1. A method for predicting the geometric morphology and machining accuracy of ultra-precision cutting surfaces, characterized in that: The following steps are involved: Obtaining machining parameters, tool geometry parameters, and characteristic parameters of the workpiece material to be cut; Establish the cutting edge profile of the tool according to the tool geometry parameters, calculate the profile deformation caused by the elastic recovery of the material according to the processing parameters and the characteristic parameters of the workpiece material to be cut, and calculate the profile deformation caused by the plastic lateral flow according to the processing parameters, the tool geometry parameters and the characteristic parameters of the workpiece material to be cut; Based on the cutting edge profile of the tool, the deformation caused by the elastic recovery of the material, and the deformation caused by the plastic lateral flow, the correction coefficient of the morphology prediction model under different processing parameters is calculated to obtain the cutting surface geometric morphology prediction model; Optimize and modify the machining parameters, pre-compensate the elastic-plastic deformation, and obtain the final cutting surface; The cutting edge profile of the tool is established according to the tool geometric parameters, specifically: ； in, R ideal is the ideal cutting edge profile of the tool, ∆ w is the cutting edge waviness amplitude; The radius is r The ideal cutting edge profile of an arc-shaped tool can be calculated by the following formula: ； The tip angle is φ The ideal cutting edge profile of a V-tip knife can be calculated by the following formula: ； in, h is the cutting depth; The contour deformation caused by plastic lateral flow includes the reduction of microgroove width caused by plastic lateral flow and the material accumulation at the microgroove boundary caused by plastic lateral flow; The final cutting surface geometry prediction model is: ； in, f d is the correction coefficient of the prediction model regarding cutting depth, f s is the correction coefficient of the prediction model for cutting speed, f m is the correction factor of the prediction model for the workpiece material; ； Where, e 1 is the elastic recovery caused by cutting force, e 2 is the elastic recovery caused by the blunt edge; Will e 1 The elastic recovery caused by the corresponding cutting force is simplified into a linear transformation, and its maximum elastic deformation δ Use the following formula to calculate: ； Where, P is the load on the workpiece, E * is the equivalent elastic modulus, R is the radius of the equivalent sphere; Elastic recovery caused by blunt edge e 2. The springback is the same everywhere along the microstructure cross-section. e 2 is calculated using the following formula: ； Where, h min is the minimum cutting thickness, ε p is the plastic strain; According to the stress-strain relationship in the elastic-plastic deformation theory, the plastic strain is calculated , σ t is the yield strength of the workpiece, E is the elastic modulus; The calculation formula for the material accumulation height at the micro-groove boundary caused by plastic lateral flow is: ； Where, ϑ represents the equivalent half-apex angle of the diamond tool; The calculation formula for the reduction in microgroove width caused by plastic lateral flow is: ； in, k c is the correction factor, k m is a coefficient determined by the material properties, k t is a coefficient determined by the tool size, L t is the cutting width of the tool.

2. The method for predicting the geometric morphology and machining accuracy of an ultra-precision cutting surface according to claim 1, wherein: The contour deformation caused by the elastic recovery of the material includes the elastic recovery caused by the cutting force and the elastic recovery caused by the blunting of the cutting edge.

3. The method for predicting the geometric morphology and machining accuracy of an ultra-precision cutting surface according to claim 1, wherein: The tool geometric parameters include the arc radius of the arc tool, the angle of the V-shaped tip, the front angle and the back angle of the tool, and the waviness of the cutting edge profile.

4. The method for predicting the geometric morphology and machining accuracy of an ultra-precision cutting surface according to claim 1, wherein: The characteristic parameters of the workpiece material to be cut include elastic modulus, Poisson's ratio, hardness and yield strength.

Images