Surface quality optimization method for tilt milling of weak rigid features based on analytical force model

Abstract

A method for optimizing the surface quality of tilted milling of weak rigid features based on an analytical force model. Through an accurate tilted milling force model, the tool is tilted to an appropriate tilt angle when milling the edge of a rigid plate to reduce the cutting force component along the direction of the lowest rigidity of the thin-walled plate, thereby significantly reducing the vibration in the milling process of thin-walled parts and effectively improving the quality of the machined surface. The present invention does not require a reduction in feed rate, does not reduce production efficiency, and does not require the introduction of additional high-cost dampers.

Description

Technical Field

[0001] The present invention relates to a technology in the field of milling, in particular to a method for optimizing the surface quality of weak rigidity characteristic inclined milling based on an analytical force model. Background Art

[0002] Milling of thin-walled features (such as aerospace cabins, end frames, rudder surfaces, wing surfaces, and engine blades) is very common in various industries, including the aerospace industry. Machining vibration often leaves irregular, deep and shallow vibration marks on the surface, resulting in poor surface aesthetics, reduced part geometry, limited machining efficiency, and shortened tool life.

[0003] Existing technologies can reduce forced vibration to a certain extent by optimizing the feed rate, but this will result in relatively low material removal rate and production efficiency. On the other hand, although dampers can be used to suppress vibration, the introduction of additional auxiliary equipment, special fixtures or customized milling cutters not only highly increases the processing cost, but also introduces uncertainty and complexity to the entire tool-workpiece-machine tool system. Therefore, the feasibility of this method of adding dampers is very limited. Summary of the invention

[0004] Aiming at the problem of poor milling surface quality of weak rigid parts, the present invention proposes a method for optimizing the surface quality of weak rigid feature tilt milling based on an analytical force model. Through an accurate tilt milling force model, the tool is tilted to an appropriate tilt angle when milling the edge of a weak rigid plate to reduce the cutting force component along the direction of the lowest rigidity of the thin-walled plate, thereby significantly reducing the vibration in the milling process of thin-walled parts and effectively improving the quality of the processed surface. This method does not require reducing the feed rate, so it does not reduce production efficiency. The second advantage of this method is that it does not require the introduction of additional high-cost dampers.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention relates to a method for optimizing surface quality of weak rigidity feature tilt milling based on an analytical force model, comprising the following steps:

[0007] Step 1) Establish an analytical model of milling force during tilt milling of weak rigid features to predict the instantaneous milling force, including:

[0008] 1.1) Determine the micro-element milling force under the tool cutting edge coordinate system P-X1Y1Z1 Where: β is the helix angle of the tool used in the milling process, K rk ,K nk ,K tkare the cutting force coefficients related to the workpiece material, h c (t,z) is the undeformed chip thickness, which is a function of time t and tool axial height z, and dz is the tool axial microelement.

[0009] The cutting force coefficient is obtained by using but not limited to the method in “Analytical models for high performance milling. Part I: Cutting forces, structural deformations and tolerance integrity” (Budak E.; Int. J. Mach. Tools Manuf., 2006, 46 (12): 1478-1488).

[0010] 1.2) The micro-element milling force under the tool spiral blade coordinate system P-X1Y1Z1 Transform to tool coordinate system O t -X t Y t Z t Micro-element milling force under in: It is the angular position of a certain element P on the cutting edge of the tool at the processing time t (the instantaneous immersion angle of the tool).

[0011] 1.3) Determine the instantaneous immersion angle of the blade element Among them: n is the spindle speed, R is the tool radius.

[0012] 1.4) Determine the dynamic undeformed chip thickness Where: f z is the feed per tooth of the tool, variable φ begin and φ end They are the corresponding rotation angles when the tool cuts in and out.

[0013] 1.5) Determine φ begin ,φ end And the integral upper and lower limits of the micro-element milling force in: h is the thickness of the thin-walled workpiece, θ is the tool inclination angle, R is the tool groove radius, and a e is the cutting width, z d It is the reference point height and can be set to 0.

[0014] 1.6) Convert the micro-element milling force in the tool coordinate system to the workpiece coordinate system and perform numerical integration to obtain the total milling force in the workpiece coordinate system: Specifically:

[0015] Step 2) Construct the geometric quality evaluation parameters of the machined surface based on the analytical model of milling force established in step 1) in: t d It is the reference time for just entering the cutting area and can be set to 0.

[0016] Step 3) optimizes the surface geometry quality evaluation parameters established in step 2), that is, the objective function is min[f(θ)], and the optimization space is θ∈[θ d ,θ u ], and get the optimal tool inclination angle θ opt , which is the tool inclination angle that minimizes milling vibration and surface roughness.

[0017] The optimization is achieved through the golden section algorithm.

[0018] The present invention relates to a system for realizing the above-mentioned method, comprising: an inclined milling cutting force model establishing unit, a model solving unit, a tool inclination angle golden section optimization unit based on minimum cutting force, and an optimization implementation unit, wherein: the inclined milling cutting force model establishing unit models the geometric interference relationship between the actual milling cutter and the workpiece to obtain an analytical model of the dynamic milling force in the inclined milling process; the model solving unit numerically calculates the analytical model according to the actual processing parameters and the tool geometric parameters to obtain a numerical solution of the cutting force in the milling process; the tool inclination angle golden section optimization unit obtains the corresponding cutting forces under different tool inclination angles and the optimal tool axis inclination angle corresponding to the minimum cutting force based on the golden section algorithm according to different tool axis inclination angles; the optimization implementation unit performs inclined milling processing according to the optimal tool axis inclination angle to achieve surface quality optimization.

[0019] Technical Effects

[0020] The present invention aims to solve the problem of poor surface quality of weak rigid parts by tilting the tool to an appropriate tilt angle when milling the edge of a rigid plate to reduce the cutting force component along the direction of the lowest rigidity of the thin-walled plate, thereby reducing machining vibration and effectively improving the quality of the machined surface. The present invention can monitor the milling force during machining in real time online by using a prediction model of the milling force during tilted milling. Based on an evaluation model that measures the vibration energy of external input in the direction of the weakest rigidity of thin-walled parts, the golden section algorithm is used to obtain the optimal tool tilt angle, so that the surface quality of the thin-walled parts after machining is the highest. This method can provide practical guidance for achieving high-quality machined surfaces in milling operations of thin-walled workpieces. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of the milling force model for the side of a thin-walled workpiece;

[0022] In the figure: (a) is the blade micro-unit, (b) is the Zt axial view, and (c) is the projection of the micro-element milling force to the tool cutting edge coordinate system PX t Y t Z t , (d) is the transformation of the micro-element milling force in the tool cutting edge coordinate system to the tool coordinate system O t -X t Y t Z t ;

[0023] Figure 2 Schematic diagram of the thickness of the undeformed chip during the side tilt milling of thin-walled parts;

[0024] Figure 3 (a) Schematic diagram of the calculation of the tool-workpiece contact relationship for the side tilt milling of thin-walled workpieces; Figure 3 (b) is an enlarged view of the tool-workpiece contact area;

[0025] Figure 4 A flowchart for calculating the optimal tool tilt angle based on the golden section search algorithm;

[0026] Figure 5 Schematic diagram of the comparison of experimentally measured and predicted cutting forces when (a) the tool inclination angle θ = 30° and (b) θ = 50°;

[0027] Figure 6 (a) Schematic diagram of the change of the value of the evaluation model f(θ) with the tool inclination angle θ; (b) Schematic diagram of the relationship between the milling force Fz and time under different tool inclination angles θ;

[0028] Figure 7 Schematic diagram of the change of vibration amplitude and evaluation index f with tool tilt angle;

[0029] Figure 8 Schematic diagram of machined surface roughness at different tilt angles;

[0030] Fig. 9 Schematic diagram of the machined surface morphology at different tool inclination angles;

[0031] Fig.10 The following is a schematic diagram of an application scenario of an embodiment. DETAILED DESCRIPTION

[0032] This embodiment relates to a method for optimizing surface quality of tilted milling of weak rigid features based on an analytical force model, comprising the following steps:

[0033] Step 1) Establish an analytical model of the milling force during tilt milling of weak rigid features to predict the instantaneous milling force, that is, the total milling force in the workpiece coordinate system Specifically:

[0034] Step 2) Construct the geometric quality evaluation parameters of the machined surface based on the analytical model of milling force established in step 1) in: t d It is the reference time for just entering the cutting area and can be set to 0.

[0035] Step 3) optimizes the surface geometry quality evaluation parameters established in step 2), that is, the objective function is min[f(θ)], and the optimization space is θ∈[θ d ,θ u ], and get the optimal tool inclination angle θ opt , which is the tool inclination angle that minimizes milling vibration and surface roughness.

[0036] like Figure 1 The figure shows the schematic diagram of the milling force model for the side of a thin-walled workpiece. The milling force model is constructed using the discrete element method. In the three-dimensional space coordinate system, the micro-element cutting force acting on the cutting edge is It is related to time t and coordinate z, specifically: in: is the cutting force coefficient related to the workpiece material, db c is the undeformed chip width, h c (t,z) is the undeformed chip thickness. Figure 1 As shown, the undeformed chip width db c Related to the tool helix angle β: db c =secβ·dz. In order to superimpose the milling forces at different points on the cutting edge, the instantaneous milling force of the micro unit is Convert to the tool helical blade coordinate system P-X1Y1Z1 Where: Transformation matrix

[0037] like Figure 1 As shown, the tool coordinate system O t -X t Y t Z t Micro-cutting force under By calculation Get, where: transformation matrix It is the angular position of a certain element P on the cutting edge of the tool at the processing time t (the instantaneous immersion angle of the tool).

[0038] The transformation matrix The instantaneous immersion angle of the tool in Where: n is the spindle speed, φ(z) is the lag angle of the tool edge element P relative to the reference point B

[0039] like Figure 2 As shown, the dynamic undeformed chip thickness h c (t,z) is the geometric interference between the cutting edge and the workpiece when the tool rotates and feeds, and the undeformed chip thickness at a certain microelement P on the cutting edge Where: f a is the equivalent feed per tooth of the tool, It is the real-time angular position of the cutting edge element P.

[0040] like Figure 3 As shown in (a), as the tool rotates, the edge element P will continuously go through three stages: air cutting, cutting, and air cutting again. The equivalent feed per tooth of the corresponding tool tooth is Where: f z is the feed per tooth of the tool, φ begin is the tool angular position when the cutting edge element P just cuts into the workpiece, φ end is the angular position of the cutting edge when the infinitesimal element P just cuts out the workpiece, and the variable φ begin and φ end Depends on the shape boundary of the tool-workpiece contact area.

[0041] The boundary of the tool-workpiece contact zone is determined by the following method to further determine the tool cutting angle φ begin and cut-out angle φ end , and the integral upper and lower limits of the micro-element milling force: the tool-workpiece contact area is a polygon BM2EM1. When the tool rotates, the reference point B will first contact the workpiece. The reference point B is at Z t The coordinate on the axis is z d Point E is the upper boundary point on the tool edge in the tool-workpiece contact area (the upper limit of the integral of the micro-element milling force). t Axis coordinate marking Where: h is the thickness of the thin-walled workpiece, θ is the tool inclination angle, R is the tool groove radius, a e is the cutting width, and the moment when the cutter teeth just cut into the contact area is t d , the moment when the contact area is cut out is t u During this period, the cutting edge passes through the two vertices M1 and M2 of the tool-workpiece contact zone in an orderly manner. Points M1 and M2 are at Z tThe coordinates of the axes z1 and z2 are: The moment when the tool tip leaves the contact area can be obtained

[0042] Due to φ begin and φ end Z of the tool edge micro-point P t The axis coordinates are directly related to the Z coordinates of vertices M1 and M2. t After axis coordinates,

[0043] like Figure 1 As shown, the tool coordinate system O t -X t Y t Z t Micro-cutting force under Transform to workpiece coordinate system O w -X w Y w Z w Micro-cutting force under Where: Transformation matrix

[0044] The micro-element cutting force Z along the tool-workpiece contact zone t The workpiece coordinate system O can be obtained by integrating the axis w -X w Y w Z w Total milling force under Specifically: Get the milling force acting on the workpiece

[0045] like Figure 3 As shown in (b), the thickness of the thin-walled workpiece is Z w The stiffness in the X direction is the worst, much lower than w and Y w Therefore, the cutting force component F along the thickness direction of the workpiece zw (t) is the main factor that determines the degree of machining vibration and deformation of the workpiece. Because machining vibration and deformation further affect the quality of the machined surface, F zw (t) also ultimately determines the smoothness of the inclined milling surface of thin-walled parts. zw (t) describes the relationship between the instantaneous value of the milling force and time. zw (t) is also related to the tool inclination angle θ, so F zw (t) can be written as F zw(t,θ). Based on the milling force analytical model established above, the geometric quality evaluation parameters of the machined surface are proposed. This model reflects the energy input into the workpiece and quantifies the cutting force F during material removal. zw The deviation of (t,θ) along the time axis can reflect the degree of machining vibration of the workpiece to a certain extent. The model can be used to evaluate the influence of the tool inclination angle θ on the machining vibration, and thus evaluate the machining surface quality of the workpiece. When f(θ) decreases, the machining vibration will decay and the milling surface quality will be improved.

[0046] According to the established surface geometry quality evaluation model f(θ) and its significance to vibration suppression, there should be an optimal milling cutter inclination angle θ opt , so that f(θ) is the smallest, that is, the vibration can be minimized or avoided at this inclination angle. Obviously, the value of the evaluation model f(θ) is non-negative, and the theoretical minimum value of f(θ) is equal to zero. From the expression of the evaluation model f(θ), the optimal milling cutter inclination angle θ is obtained. opt It is difficult to find the analytical expression of . Therefore, a mathematical optimization model is introduced to find the optimal tilt angle, and numerical calculations are performed using MATLAB software. The objective function and constraints for the optimization are

[0047] According to the mathematical form of the evaluation model f(θ), it can be known that the model is a one-dimensional concave function. In order to find the optimal solution to the minimization problem of this single variable function, the golden section algorithm based on numerical calculation is used. The principle of this algorithm is to symmetrically obtain a series of golden section points from the variable interval of the single variable function according to the golden ratio 0.618. After that, the corresponding function values ​​of each section point are calculated and compared. Then, by gradually narrowing the given variable interval, the optimal solution of the function can be determined. Figure 4 As shown, the optimum tool tilt angle will be [θ d, θ u ] range until the given iteration accuracy ε is met.

[0048] Based on the proposed thin-walled plate inclined side milling cutting force model, the machined surface geometric quality evaluation model f(θ) and the above optimization strategy, the optimal tool inclination angle θ for improving the machined surface quality when inclined side milling the edge of a thin-walled plate can be obtained. opt .

[0049] After specific practical experiments, the cutting tool used is a solid carbide milling cutter with a diameter of 12mm, 4 teeth, a front angle of 6°, a back angle of 11°, and a helix angle of 30°. The workpiece material is 6061 aluminum alloy. The milling force is measured by a Kistler 9272 dynamometer. Experimental parameters: spindle speed n = 1000rpm, radial cutting width ae = 0.2mm, feed speed f = 280mm / min, milling method is reverse milling, and the tool inclination angle θ is set to 6 levels: 0°, 10°, 20°, 30°, 40°, 50°. The cantilever length of the thin-walled part is 8mm.

[0050] During the milling process, the laser displacement measurement sensor CD5L-25 is used to collect the instantaneous vibration displacement during the milling of thin-walled plates.

[0051] After milling, the surface roughness was measured with a surface roughness tester (Mitutoyo SJ-210), and the surface morphology was photographed with an optical microscope (Keyence VHX-600). The cutting force and vibration displacement of the thin wall during the machining process, as well as the surface roughness and surface morphology after machining were analyzed.

[0052] like Figure 5 As shown, it is a comparison between the milling force predicted by this method and the milling force measured experimentally when the tool inclination angle θ=30° and θ=50°. It can be found that the prediction results and the experimental results are in good agreement in the following aspects: (i) The waveforms of the predicted results and the experimental results are consistent, indicating that when the tool rotates from 0 degrees to 360 degrees, the change trends of the predicted value and the experimental value are consistent. (ii) The periods of the cutting force waveforms of the predicted results and the experimental results are equal, which means that the theoretical model is capable of describing the periodic characteristics of the milling force. (iii) The instantaneous values ​​of the cutting force waveforms of the predicted results and the experimental results are close. The above analysis shows that the prediction model of the milling force in the inclined side milling process of thin-walled parts proposed in this embodiment is accurate and reliable.

[0053] Optimize the milling cutter inclination angle to reduce vibration during side milling of thin-walled workpieces. According to the established evaluation model f(θ) and the proposed optimization strategy, under a given iteration accuracy ε = 2 degrees, the change of the evaluation index f(θ) with the tool inclination angle θ can be obtained, as shown in Figure 6 (a). At the same time, according to the established milling force model, F z The change curve of Figure 6 (b) As shown in the figure, as the tool inclination angle increases, the f(θ) value first decreases, and then increases almost linearly. When the inclination angle θ = 22 degrees, f(θ) reaches the minimum value of 0.08N. Therefore, θ = 22 degrees is considered to be the best tool inclination angle for vibration suppression. In addition, it can be found that as the tool inclination angle increases, the change trend of f(θ) is similar to that of F zThe absolute value of the peak value of F is very consistent. When the optimal tool inclination angle is 22 degrees, z The value of is close to zero, which means that the vibration induced by the cutting force is the weakest and the surface quality is the highest in this case. Based on the above discussion, the predicted optimal tool inclination angle is 22 degrees.

[0054] In order to verify the above prediction results, the surface roughness, surface topography and instantaneous vibration displacement during machining under different tool inclination angles were obtained through experiments. The influence of tool inclination angle on suppressing workpiece vibration was studied, and the correctness of the established evaluation model was verified.

[0055] like Figure 7 As shown, the vibration amplitude and the corresponding evaluation index f(θ) vary with the tool inclination angle. At the predicted optimal inclination angle (22 degrees), the amplitude of the vibration displacement reached a minimum value of 15.2 μm in all experiments. As the inclination angle increases, the vibration amplitude and the evaluation index f(θ) have the same change trend. At the predicted optimal inclination angle (22 degrees), both variables reach their minimum values. Therefore, it can be confirmed that the proposed evaluation model f(θ) can accurately measure the vibration degree of the workpiece, and the optimization strategy proposed in this embodiment can produce a good vibration suppression effect on the processing of weak rigidity thin-walled workpieces.

[0056] like Figure 8 As shown in the figure, surface roughness is closely related to vibration, and the larger machined surface roughness is caused by the larger vibration of the workpiece during milling. After experiments, the machined surface roughness Ra, Rq and Rz were measured at different tool inclination angles and the predicted optimal inclination angle of 22 degrees. It can be seen that at an inclination angle of 22 degrees, Ra and Rq reached the minimum values ​​of 0.47μm and 0.58μm, while Rz reached the second minimum value of 3.14μm. Among the angles studied, the inclination angle of 22 degrees is the best for machining surface finish. The experimental results show that the tool axis rake angle obtained based on this method can produce a good vibration suppression effect on the machining of weak rigid thin-walled workpieces and improve the quality of the machined surface. The feasibility of the proposed evaluation model f(θ) to optimize surface finish is proved.

[0057] like Fig. 9 As shown in the figure, the morphology of the machined surface is different under the tool inclination angle studied. Uniformly distributed and mutually parallel stripes can be clearly observed on these surfaces. The angle between the stripes and the perpendicular to the tool feed direction is equal to the tool inclination angle, indicating that these stripes are caused by the periodic cutting of the milling tool. Among these surface morphologies, it is obvious that the surface morphology when the tool inclination angle is 22 degrees has more regular textures and fewer vibration marks than the other surface morphologies. This phenomenon shows that the weakest workpiece vibration and the best surface quality can be obtained when the tool inclination angle is 22 degrees.

[0058] Compared with the existing technology, this method introduces the tool axis inclination angle in the model, and the instantaneous undeformed cutting thickness Cutting angle of tool φ begin and cut-out angle φ end , the integral upper limit z of the micro-element milling force d and lower limit The geometry of the tool-workpiece contact zone and the transformation matrix of the cutting force in the workpiece coordinate system and the tool coordinate system are all related to the tool inclination angle θ. In other words, after considering the tool inclination angle θ, the model can reflect the energy input into the workpiece and quantify the cutting force F during the material removal process. zw The deviation of (t,θ) along the time axis can reflect the degree of machining vibration of the workpiece to a certain extent and thus reflect the surface quality of milling. It is more in line with the actual machining situation and can predict the milling force when the tool is tilted. In actual machining, it is no longer necessary to purchase acceleration sensors to measure the vibration in milling. However, the traditional theoretical model that does not consider the tool tilt angle cannot predict the milling force when the tool is tilted.

[0059] In summary, this method targets the problem of poor milling surface quality of weak rigid parts and can provide practical guidance for achieving high-quality machined surfaces in milling operations of thin-walled workpieces.

[0060] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for optimizing surface quality of tilted milling of weak rigid features based on analytical force model, characterized in that: The steps include: Step 1) Establish an analytical model of the milling force during tilt milling of weak rigid features to predict the instantaneous milling force, that is, the total milling force in the workpiece coordinate system Specifically: Specifically include: 1.1) Determine the micro-element milling force under the tool cutting edge coordinate system P-X1Y1Z1 Where: β is the helix angle of the tool used in the milling process, K rk ,K nk ,K tk are the cutting force coefficients related to the workpiece material, h c (t,z) is the undeformed chip thickness, which is a function of time t and tool axial height z, and dz is the tool axial microelement; 1.2) The micro-element milling force under the tool spiral blade coordinate system P-X1Y1Z1 Transform to tool coordinate system O t -X t Y t Z t Micro-element milling force under in: is the angular position of a microelement P on the cutting edge of the tool at the machining time t, that is, the instantaneous immersion angle of the tool; 1.3) Determine the instantaneous immersion angle of the blade element Where: n is the spindle speed, R is the tool radius; 1.4) Determine the dynamic undeformed chip thickness Where: f z is the feed per tooth of the tool, variable φ begin and φ end They are the corresponding rotation angles when the tool cuts in and out respectively; 1.5) Determine φ begin ,φ end And the integral upper and lower limits of the micro-element milling force in: h is the thickness of the thin-walled workpiece, θ is the tool inclination angle, R is the tool groove radius, and a e is the cutting width, z d is the reference point height; 1.6) Convert the micro-element milling force in the tool coordinate system to the workpiece coordinate system and perform numerical integration to obtain the total milling force in the workpiece coordinate system: Specifically: Step 2) Construct the geometric quality evaluation parameters of the machined surface based on the analytical model of milling force established in step 1) in: t d It is the reference time just entering the cutting area; Step 3) optimizes the surface geometry quality evaluation parameters established in step 2), that is, the objective function is min[f(θ)], and the optimization space is θ∈[θ d ,θ u ], and get the optimal tool inclination angle θ opt , which is the tool inclination angle that minimizes milling vibration and surface roughness; The optimization is achieved through the golden section algorithm, specifically: after a series of golden section points are symmetrically obtained from the variable interval of the single variable function according to the golden ratio 0.618, the corresponding function values ​​of each section point are calculated and compared; then the optimal solution of the function is determined by gradually narrowing the given variable interval.

2. A weak rigidity feature tilt milling surface quality optimization system for implementing the method described in claim 1, characterized in that: include: The inclined milling cutting force model establishment unit, the model solving unit, the tool inclination angle golden section optimization unit based on the minimum cutting force and the optimization implementation unit, wherein: the inclined milling cutting force model establishment unit models the actual geometric interference relationship between the milling cutter and the workpiece to obtain the analytical model of the dynamic milling force in the inclined milling process; the model solving unit numerically calculates the analytical model according to the actual processing parameters and the tool geometric parameters to obtain the numerical solution of the cutting force in the milling process; the tool inclination angle golden section optimization unit obtains the corresponding cutting force under different tool inclination angles and the optimal tool axis inclination angle corresponding to the minimum cutting force based on the golden section algorithm according to different tool axis inclination angles; the optimization implementation unit performs inclined milling processing according to the optimal tool axis inclination angle to achieve surface quality optimization.

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