A workpiece radial material removal depth prediction method for flexible abrasive tools

Abstract

The application relates to the technical field of numerical control machining, and particularly discloses a workpiece radial material removal depth prediction method for a flexible grinding tool, which comprises the following steps: acquiring machining parameters of a current workpiece and a radial material removal depth theoretical value of the current workpiece, determining a maximum deformation of the current flexible grinding tool according to the radial material removal depth theoretical value of the current workpiece, obtaining a normal grinding force calculation formula of the flexible grinding tool according to Hertz elastic contact theory, establishing a workpiece radial material removal depth prediction model according to the normal grinding force calculation formula of the flexible grinding tool and a Preston equation, inputting the machining parameters of the current workpiece and the maximum deformation of the current flexible grinding tool into the workpiece radial material removal depth prediction model for prediction, and outputting a radial material removal depth prediction value of the current workpiece. The application can predict the material removal amount of the workpiece surface and provide technical guidance for flexible grinding tool machining mechanism analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of numerical control machining, more particularly, to a workpiece radial material removal depth prediction method for a flexible abrasive tool. BACKGROUND

[0002] The blisk is a new type of component designed to meet the high-performance aero-engine, which has the technical benefits of simplifying the structure, reducing the load between parts, and improving the aerodynamic efficiency. At present, the machining method of the blisk mainly relies on multi-axis numerical control milling, but due to the complex free-form surface of the blade profile, after milling, the blade surface will produce milling residual tool marks, and the residual height between the tool marks is quite different, which cannot meet the blade surface quality requirements of the blisk. Therefore, surface grinding and polishing technology needs to be developed to improve the blade surface quality of the blisk.

[0003] At present, the surface grinding and polishing of the blisk is mainly completed manually, and manual polishing not only has high labor intensity, low processing efficiency, and serious environmental pollution, but also cannot guarantee the surface precision, consistency and integrity, which seriously affects the production cycle, performance and life of the aero-engine. In order to solve the shortcomings of manual polishing, scholars at home and abroad use industrial robots and multi-axis numerical control machine tools as polishing test platforms, and multi-axis numerical control machine tools are widely used in surface precision machining due to their good rigidity and machining precision. Therefore, the multi-axis numerical control machine tool is used to study the polishing mechanism of the flexible abrasive tool. The flexible abrasive tool has the characteristics of large contact area and small polishing force, which can effectively solve the milling residual tool marks and ensure the quality of the blisk blade profile.

[0004] At present, the radial material removal modeling of the rigid abrasive tool is relatively perfect, and the radial material removal modeling of the flexible abrasive tool as another effective polishing tool is not mature, and needs further in-depth study. SUMMARY

[0005] The present application provides a workpiece radial material removal depth prediction method for a flexible abrasive tool to solve the problem of lack of radial material removal depth modeling of the flexible abrasive tool in the related art.

[0006] As a first aspect of the present application, a workpiece radial material removal depth prediction method for a flexible abrasive tool is provided, comprising the following steps:

[0007] Step S1: Obtain the machining parameters of the current workpiece and the theoretical value of the radial material removal depth of the current workpiece, and determine the maximum deformation of the current flexible abrasive tool according to the theoretical value of the radial material removal depth of the current workpiece;

[0008] Step S2: Obtain the normal grinding force calculation formula of the flexible abrasive tool according to the Hertz elastic contact theory;

[0009] Step S3: establishing a workpiece radial material removal depth prediction model according to the normal grinding force calculation formula of the flexible grinding tool and the Preston equation;

[0010] Step S4: inputting the machining parameters of the current workpiece and the maximum deformation of the current flexible grinding tool into the workpiece radial material removal depth prediction model for prediction, to output a radial material removal depth prediction value of the current workpiece.

[0011] Further, the normal grinding force calculation formula of the flexible grinding tool obtained according to the Hertz elastic contact theory comprises:

[0012] The normal grinding force F of the flexible grinding tool n The calculation formula is as follows:

[0013]

[0014] Wherein, b is the contact height of the flexible grinding tool and the workpiece, a is the contact half-width of the flexible grinding tool and the workpiece, v w is the Poisson's ratio of the workpiece, E w is the elastic modulus of the workpiece, v b is the Poisson's ratio of the flexible grinding tool, E b is the elastic modulus of the flexible grinding tool, R1 is the radius of the flexible grinding tool, and R2 is the curvature radius of the workpiece at the contact point of the flexible grinding tool and the workpiece.

[0015] Further, the calculation formula of the contact half-width a of the flexible grinding tool is as follows:

[0016]

[0017] Wherein, δ max is the maximum deformation of the flexible grinding tool, and the numerical value of the maximum deformation of the flexible grinding tool is equal to the theoretical value of the radial material removal depth of the workpiece.

[0018] Further, the workpiece radial material removal depth prediction model is established according to the normal grinding force calculation formula of the flexible grinding tool and the Preston equation, which comprises:

[0019] The Preston equation is as follows:

[0020]

[0021] Wherein, h is the radial material removal depth of the workpiece; K is the Preston coefficient; V is the relative motion speed of the flexible grinding tool and the workpiece; P is the pressure, F n is the normal grinding force of the flexible grinding tool, and A is the contact area of the flexible grinding tool and the workpiece, wherein A = 2ab.

[0022] The average radial material removal rate of the workpiece within the contact area between the flexible abrasive and the workpiece is taken as the radial material removal rate H of the workpiece. m The radial material removal rate H of the workpiece obtained according to the Preston equation m The calculation formula is:

[0023] H m =KP m V m

[0024] Among them, P m For average pressure, V m The average relative velocity between the flexible abrasive and the workpiece;

[0025] Based on the radial material removal rate H of the workpiece m The radial material removal depth prediction model a for the workpiece is obtained. p The workpiece radial material removal depth prediction model a p for:

[0026]

[0027] Where S is the feed rate and dL is the unit length.

[0028] Furthermore, based on the different curvature changes of the workpiece surface, the contact methods between the flexible abrasive and the workpiece are divided into convex surface contact and concave surface contact;

[0029] (1) Radial material removal rate H of the workpiece during convex surface contact m1 The calculation formula is:

[0030] H m1 =KP m1 V1

[0031] Among them, the average pressure P m1 The formulas for calculating the average relative velocity V1 are as follows:

[0032]

[0033]

[0034] The radial material removal rate H of the workpiece m1 The calculation formula is:

[0035]

[0036] (2) Radial material removal rate H of the workpiece during concave contact m2 The calculation formula is:

[0037] Hm2 = KP m2 V2

[0038] wherein the average pressure P m2 and the average relative motion speed V2 are calculated by the following formulas respectively:

[0039]

[0040]

[0041] and the radial material removal rate H m2 of the workpiece is calculated by the following formula:

[0042]

[0043] wherein n is the spindle speed of the flexible abrasive tool; and x is the coordinate of each point in the contact area of the flexible abrasive tool and the workpiece along the feeding direction.

[0044] Further, the inputting of the machining parameter of the current workpiece and the maximum deformation of the current flexible abrasive tool into the workpiece radial material removal depth prediction model for prediction to output the radial material removal depth prediction value of the current workpiece further comprises:

[0045] the inputting of the machining parameter of the current workpiece and the maximum deformation of the current flexible abrasive tool into the workpiece radial material removal depth prediction model for calculation to calculate the radial material removal depth prediction value of the current workpiece.

[0046] wherein the machining parameter of the current workpiece comprises the Poisson's ratio of the current workpiece, the elastic modulus of the current workpiece, the radius of curvature of the current workpiece, the Poisson's ratio of the current flexible abrasive tool, the elastic modulus of the current flexible abrasive tool, the radius of the current flexible abrasive tool, the spindle speed of the current flexible abrasive tool and the feeding speed.

[0047] The workpiece radial material removal depth prediction method for the flexible abrasive tool provided by the application has the following beneficial effects: according to the Hertz elastic contact theory and the Preston equation, the relationship between the radial theoretical material removal depth and the actual material removal depth is derived, and according to the material removal conservation principle, the radial material removal depth model is obtained, which lays a foundation for the research on the polishing mechanism of the flexible abrasive tool. BRIEF DESCRIPTION OF DRAWINGS

[0048] The accompanying drawings are included to provide a further understanding of the application, and constitute a part of the specification, and are used together with the specific embodiments described below to explain the application, but do not constitute a limitation on the application.

[0049] Figure 1 The flowchart of the workpiece radial material removal depth prediction method for the flexible abrasive tool provided by the application is shown in the figure.

[0050] Figure 2 The trend diagram of the flexible abrasive provided by the present invention as a function of spindle speed.

[0051] Figure 3 This is a schematic diagram of the flexible abrasive structure provided by the present invention.

[0052] Figures 4a to 4b This is a schematic diagram of the contact between the convex and concave surfaces provided by the present invention.

[0053] Figures 5a to 5b Error curves of the removal depth prediction results for surface grinding and cylindrical grinding provided by the present invention.

[0054] Figures 6a to 6b The curve showing the influence of the process parameters provided by this invention on the radial material removal depth of the workpiece. Detailed Implementation

[0055] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a workpiece radial material removal depth prediction method for flexible abrasives proposed according to the present invention. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0056] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of the invention described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0057] This embodiment provides a method for predicting the radial material removal depth of a workpiece for flexible abrasives, such as... Figure 1 As shown, the method for predicting the radial material removal depth of a workpiece for flexible abrasives includes the following steps:

[0058] Step S1: Obtain the machining parameters of the current workpiece and the theoretical value of the radial material removal depth of the current workpiece, and determine the maximum deformation of the current flexible mold based on the theoretical value of the radial material removal depth of the current workpiece;

[0059] Step S2: Obtain the formula for calculating the normal grinding force of the flexible grinding wheel based on Hertz's elastic contact theory;

[0060] Preferably, the formula for calculating the normal grinding force of the flexible grinding wheel based on Hertz's elastic contact theory includes:

[0061] The normal grinding force F of the flexible abrasive tool n The calculation formula is as follows:

[0062]

[0063] Where b is the contact height between the flexible abrasive and the workpiece, a is the half-width of the contact between the flexible abrasive and the workpiece, and v w E represents the Poisson's ratio of the workpiece. w v is the elastic modulus of the workpiece. b E represents the Poisson's ratio of flexible abrasives. b R1 is the elastic modulus of the flexible abrasive, R2 is the radius of the flexible abrasive, and R2 is the workpiece curvature radius at the contact point between the flexible abrasive and the workpiece.

[0064] Specifically, the formula for calculating the contact half-width 'a' between the flexible abrasive and the workpiece is as follows:

[0065]

[0066] Where, δ max The maximum deformation of the flexible abrasive is equal to the theoretical value of the radial material removal depth of the workpiece.

[0067] Step S3: Establish a prediction model for the radial material removal depth of the workpiece based on the calculation formula of the normal grinding force of the flexible abrasive and the Preston equation;

[0068] Preferably, the step of establishing a workpiece radial material removal depth prediction model based on the calculation formula of the normal grinding force of the flexible abrasive and the Preston equation includes:

[0069] The Preston equation is as follows:

[0070]

[0071] Where h is the radial material removal depth of the workpiece; K is the Preston coefficient, determined by the properties of the abrasive and workpiece materials; V is the relative speed between the flexible abrasive and the workpiece; and P is the pressure. Fn The normal grinding force of the flexible abrasive is A, and the contact area between the flexible abrasive and the workpiece is A = 2ab.

[0072] During the processing, the material removal rate in the contact area between the flexible abrasive and the workpiece exhibits a parabolic distribution. For ease of study, the average radial material removal rate of the workpiece within the contact area between the flexible abrasive and the workpiece is taken as the radial material removal rate H. m The radial material removal rate H of the workpiece obtained according to the Preston equation m The calculation formula is:

[0073] H m =KP m V m

[0074] Among them, P m For average pressure, V m The average relative velocity between the flexible abrasive and the workpiece;

[0075] Based on the principle of equal material removal during flexible abrasive machining and the radial material removal rate H of the workpiece m The radial material removal depth prediction model a for the workpiece is obtained. p The workpiece radial material removal depth prediction model a p for:

[0076]

[0077] Where S is the feed rate and dL is the unit length.

[0078] Specifically, based on the different curvature changes of the workpiece surface, the contact methods between the flexible abrasive and the workpiece are divided into convex surface contact and concave surface contact, such as... Figures 4a to 4b As shown;

[0079] (1) As Figure 4a As shown, the radial material removal rate H of the workpiece during convex surface contact m1 The calculation formula is:

[0080] H m1 =KP m1 V1

[0081] Among them, the average pressure P m1 The formulas for calculating the average relative velocity V1 are as follows:

[0082]

[0083]

[0084] The radial material removal rate H of the workpiece m1The calculation formula is:

[0085]

[0086] (2) Figure 4b As shown, the radial material removal rate H of the workpiece during concave-surface contact is... m2 The calculation formula is:

[0087] H m2 =KP m2 V2

[0088] Among them, the average pressure P m2 The formulas for calculating the average relative velocity V2 are as follows:

[0089]

[0090]

[0091] The radial material removal rate H of the workpiece m2 The calculation formula is:

[0092]

[0093] Where n is the spindle speed of the flexible abrasive; x is the coordinate of each point in the contact area between the flexible abrasive and the workpiece along the feed direction.

[0094] Step S4: Input the machining parameters of the current workpiece and the maximum deformation of the current flexible mold into the radial material removal depth prediction model of the workpiece for prediction, so as to output the radial material removal depth prediction value of the current workpiece.

[0095] Preferably, the step of inputting the machining parameters of the current workpiece and the maximum deformation of the current flexible abrasive into the radial material removal depth prediction model of the workpiece for prediction, so as to output the predicted value of the radial material removal depth of the current workpiece, further includes:

[0096] The machining parameters of the current workpiece and the maximum deformation of the current flexible mold are substituted into the radial material removal depth prediction model of the workpiece for calculation, so as to calculate the predicted value of the radial material removal depth of the current workpiece.

[0097] The processing parameters of the current workpiece include the Poisson's ratio, the elastic modulus, the radius of curvature of the current workpiece, the Poisson's ratio, the elastic modulus, the radius, the spindle speed, and the feed rate of the current flexible grinding wheel.

[0098] The present invention provides a method for predicting the radial material removal depth of a workpiece for flexible abrasives. Based on Hertz elastic contact theory, a formula for calculating the normal grinding force is established, and the Preston equation is used to establish a model for predicting the radial material removal depth, thereby laying the foundation for the study of the polishing mechanism of flexible abrasives.

[0099] It should be noted that, based on the changes in spindle speed, workpiece radius of curvature, and radial theoretical grinding depth, the influence of different processing parameters on the predicted value of radial material removal depth of the workpiece is analyzed.

[0100] It should be noted that, considering the large deformation of the flexible mold, the radius of the flexible mold needs to be calibrated while the spindle is idling. Figure 2 As shown, the relationship between the flexible grinding tool and the spindle speed is such that the radius of the flexible grinding tool increases linearly with the increase of the spindle speed.

[0101] like Figure 3 As shown, this invention uses a flap wheel as an example to model the radial material removal depth.

[0102] The present invention describes the Taguchi orthogonal grinding experiment of TC4 on a three-axis CNC machining center.

[0103] The workpiece parameters and flap wheel parameters of this invention are shown in Table 1.

[0104] Table 1. Workpiece parameters and flap wheel parameters

[0105]

[0106] The experimentally determined K coefficient values ​​are shown in Table 2 below, with an average K coefficient value of 6.633 × 10⁻⁶. -5 .

[0107] Table 2K Coefficient Values

[0108] Number n (r / min) S (mm / min) a e (mm)]]> a p (μm) K 1 6000 100 0.8 0.298 6.57 x 10 -5 ]] 2 6000 100 1.0 0.338 6.65 x 10 -5 ]]> 3 8000 100 0.8 0.301 6.74 x 10 -5 ]]> 4 8000 100 1.0 0.329 6.57 x 10 -5 ]]>

[0109] The results of the TC4 surface grinding experiment and the cylindrical surface grinding experiment are shown in Table 3 and Table 4, respectively.

[0110] Table 3. Experimental Results of TC4 Surface Grinding

[0111]

[0112] Table 4 Results of TC4 Cylindrical Surface Grinding Experiment

[0113]

[0114] like Figures 5a to 5bAs shown in Tables 3 and 4, it can be seen from the comparison that the radial material removal depth prediction method of the flexible abrasive constructed in this invention can predict the radial material removal depth value under different processing parameters very well.

[0115] like Figures 6a to 6b As shown, the horizontal axis represents influencing factors, and the vertical axis represents the predicted radial material removal depth of the workpiece. Figures 6a to 6b It can be seen that the theoretical value of radial material removal depth a e The radial material removal depth of the workpiece is the main influencing factor, and the workpiece surface curvature radius R2 is the second main influencing factor.

[0116] In summary, the radial material removal depth prediction method for flexible abrasives, applicable to workpieces, presented in this invention, can accurately predict the radial material removal depth of workpieces under different processing parameters. The theoretical grinding depth has the greatest impact on the radial material removal depth, followed by the workpiece surface radius of curvature. The method described in this paper considers the influence of different process parameters on the radial material removal depth of the workpiece. By inputting processing parameters, material parameters, and abrasive parameters, the radial material removal depth of the workpiece can be obtained, providing technical guidance for the analysis of the processing mechanism of flexible abrasives.

[0117] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting the radial material removal depth of a workpiece for use in flexible abrasives, characterized in that, Includes the following steps: Step S1: Obtain the machining parameters of the current workpiece and the theoretical value of the radial material removal depth of the current workpiece, and determine the maximum deformation of the current flexible mold based on the theoretical value of the radial material removal depth of the current workpiece; Step S2: Obtain the formula for calculating the normal grinding force of the flexible grinding wheel based on Hertz's elastic contact theory; Step S3: Establish a prediction model for the radial material removal depth of the workpiece based on the calculation formula of the normal grinding force of the flexible abrasive and the Preston equation; Step S4: Input the machining parameters of the current workpiece and the maximum deformation of the current flexible mold into the radial material removal depth prediction model of the workpiece for prediction, so as to output the radial material removal depth prediction value of the current workpiece; The formula for calculating the normal grinding force of flexible grinding wheels based on Hertz's elastic contact theory includes: The normal grinding force F of the flexible abrasive tool n The calculation formula is as follows: ， Where b is the contact height between the flexible abrasive and the workpiece, a is the half-width of the contact between the flexible abrasive and the workpiece, and v w E represents the Poisson's ratio of the workpiece. w v is the elastic modulus of the workpiece. b E represents the Poisson's ratio of flexible abrasives. b R1 is the elastic modulus of the flexible abrasive, R2 is the radius of the flexible abrasive, and R2 is the radius of curvature of the workpiece at the contact point between the flexible abrasive and the workpiece. The formula for calculating the contact half-width 'a' between the flexible abrasive and the workpiece is as follows: ， Where, δ max The maximum deformation of the flexible abrasive is equal to the theoretical value of the radial material removal depth of the workpiece. The step of establishing a workpiece radial material removal depth prediction model based on the normal grinding force calculation formula of the flexible grinding wheel and the Preston equation includes: The Preston equation is as follows: ， Where h is the radial material removal depth of the workpiece; K is the Preston coefficient; V is the relative speed between the flexible abrasive and the workpiece; and P is the pressure. F n The normal grinding force of the flexible abrasive is A, and the contact area between the flexible abrasive and the workpiece is A = 2ab. The average radial material removal rate of the workpiece within the contact area between the flexible abrasive and the workpiece is taken as the radial material removal rate H of the workpiece. m The radial material removal rate H of the workpiece obtained according to the Preston equation m The calculation formula is: ， Among them, P m For average pressure, V m The average relative velocity between the flexible abrasive and the workpiece; Based on the radial material removal rate H of the workpiece m Obtain the workpiece radial material removal depth prediction model The workpiece radial material removal depth prediction model for: ， Where S is the feed rate and dL is the unit length.

2. The method for predicting the radial material removal depth of a workpiece for flexible abrasives according to claim 1, characterized in that, Based on the different curvature changes of the workpiece surface, the contact methods between flexible abrasives and workpieces are divided into convex surface contact and concave surface contact. (1) Radial material removal rate H of the workpiece during convex surface contact m1 The calculation formula is: ， Among them, the average pressure P m1 The formulas for calculating the average relative velocity V1 are as follows: ， ， The radial material removal rate H of the workpiece m1 The calculation formula is: ， (2) Radial material removal rate H of the workpiece when the concave surface is in contact m2 The calculation formula is: ， Among them, the average pressure P m2 The formulas for calculating the average relative velocity V2 are as follows: ， ， The radial material removal rate H of the workpiece m2 The calculation formula is: ， Where n is the spindle speed of the flexible abrasive; x is the coordinate of each point in the contact area between the flexible abrasive and the workpiece along the feed direction.

3. The method for predicting the radial material removal depth of a workpiece for flexible abrasives according to claim 1, characterized in that, The step of inputting the machining parameters of the current workpiece and the maximum deformation of the current flexible abrasive into the radial material removal depth prediction model of the workpiece for prediction, so as to output the predicted value of the radial material removal depth of the current workpiece, further includes: The machining parameters of the current workpiece and the maximum deformation of the current flexible mold are substituted into the radial material removal depth prediction model of the workpiece for calculation, so as to calculate the predicted value of the radial material removal depth of the current workpiece. The processing parameters of the current workpiece include the Poisson's ratio, the elastic modulus, the radius of curvature of the current workpiece, the Poisson's ratio, the elastic modulus, the radius, the spindle speed, and the feed rate of the current flexible grinding wheel.

Images