Method for predicting wear width of rear tool face of tool based on milling force on machining site

Abstract

The invention discloses a tool flank wear width prediction method based on a milling force on a machining site, and relates to the technical field of aerospace complex thin-wall part machining, and the method comprises the following steps: 1, building a shear force prediction model considering vibration and a tool flank wear effect; (2) establishing a friction force prediction model considering vibration and a tool flank wear effect; (3) establishing a milling force prediction model considering vibration and a rear cutter surface wear effect of the cutter; and (4) constructing a mapping relation model of the milling force and the wear width of the rear tool face of the tool. According to the method, the influence of vibration and the tool flank wear effect on the milling force is considered, and a more accurate tool flank wear width prediction result can be obtained.

Description

Technical Field

[0001] The present invention patent relates to a method for predicting the flank wear width of a cutting tool based on the milling force at the machining site, belonging to the technical field of machining of complex thin-walled parts in the aerospace industry, and is mainly applied to the prediction of the flank wear width of a cutting tool during the milling process of complex thin-walled parts. Background Art

[0002] With the rapid development of the aerospace industry, in order to adapt to the working environment of related equipment and meet the working performance requirements at the same time, more and more thin-walled parts are made of difficult-to-machine materials; however, during the machining process of difficult-to-machine materials, the cutting temperature is high, the dynamic load is large, and the mechanical pressure is large, which will lead to serious flank wear of the cutting tool; the tool wear causes the contact area between the tool and the workpiece to increase, resulting in an increase in the cutting force, which causes an increase in the normal stress on the flank, further aggravating the flank wear of the cutting tool; if the tool is not replaced in time after severe wear, it will directly affect the machining quality of the parts and even damage the workpiece and the machine tool; therefore, in order to improve the machining quality, machining efficiency and extend the service life of the cutting tool, accurately identifying the flank wear state of the cutting tool during machining has important engineering application value;

[0003] Under normal circumstances, the real-time monitoring methods for tool wear during the machining process are divided into direct monitoring methods and indirect monitoring methods. However, due to the continuous contact between the tool and the workpiece and the harsh machining environment, the application of direct monitoring methods in the actual machining process is greatly limited. Therefore, indirect monitoring methods are mostly used in the research of tool wear monitoring. Among the indirect monitoring methods, there are pure data methods based on deep learning and monitoring methods based on physical models. The pure data methods based on deep learning have strong data dependence, high requirements for computing resources, and limited model generalization ability. The monitoring methods based on physical models can analyze the relationship between tool wear and monitoring targets and have a clear causal mechanism. At the same time, the most significant phenomenon caused by tool wear during the machining process is the increase in cutting force. Therefore, it is very valuable to apply the milling force signal during the machining process to the prediction of the flank wear width of the tool. For the specific method, please refer to [Hou YF, Zhang DH, Wu BH, Luo M. Milling Force Modeling of Worn Tool and Tool Flank Wear Recognition in End Milling. IEEE / ASME Transactions on Mechatronics, 2015. 20(3): p. 1024 - 1035.]. This method establishes a milling force model considering tool wear effects and provides a basic model for optimizing the milling feed speed. However, during the calculation process of this model, the vibration during the machining process is not considered, and the working conditions such as the weak rigidity of parts in actual milling machining are not comprehensively considered. Therefore, further improvement is needed when applying this method to the monitoring of tool wear status during the milling machining of thin-walled parts. Based on this, the present invention is proposed. Summary of the Invention

[0004] In order to solve the problem that the existing physical model is difficult to accurately monitor the tool wear status during the milling machining of thin-walled parts, the present invention proposes a method for predicting the flank wear width of a tool based on the milling force at the machining site.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions: A method for predicting the flank wear width of a tool based on the milling force at the machining site, including the following steps:

[0006] ① Establish a shear force prediction model considering vibration and tool flank wear effects;

[0007] ② Establish a friction force prediction model considering vibration and tool flank wear effects;

[0008] ③ Establish a milling force prediction model considering vibration and tool flank wear effects;

[0009] ④Construct a mapping relationship model between the milling force and the flank wear width of the cutting tool.

[0010] The specific process of step ① is as follows:

[0011] In the space coordinate system, the cutting tool is discretized along the axial direction into several differential elements. The shear force received by the j-th tooth of the i-th differential element on the milling cutter is expressed as Equation (1):

[0012]

[0013] In the formula, K tc , K rc and K ac are the tangential, radial, and axial shear force coefficients respectively. K te , K re and K ae are the tangential, radial, and axial edge force coefficients respectively. h v,w,i,j (t) is the instantaneous undeformed chip thickness considering the effects of vibration and tool wear, which is expressed by Equation (2).

[0014] h v,w,i,j (t) = h v,i,j (t) - h w,i,j (t) (2)

[0015] In the formula: h v,i,j (t) is the instantaneous undeformed cutting thickness considering vibration, which is expressed by Equation (3); h w,i,j (t) is the influence of tool wear on the instantaneous undeformed cutting thickness, which is expressed by Equation (4).

[0016] h v,i,j (t) = h sa,i,j (t) + h dy,i,j (t) (3)

[0017]

[0018] In Equation (3), h as,i,j (t) is the static instantaneous undeformed chip thickness in the ideal cutting state, which is expressed by Equation (5); h dy,i,j (t) is the dynamic instantaneous undeformed chip thickness considering vibration, which is expressed by Equation (6).

[0019] h sa,i,j (t) = fsinφ i,j (t) (5)

[0020] h dy,i,j (t) = h Tdy,i,j (t) + h Wdy,i,j (t) (6)

[0021] In Equation (5), f is the feed per tooth, and φ i,j (t) is the instantaneous rotation angle of the i-th differential unit on the j-th tooth of the tool, which is expressed by Equation (7). In Equation (6), h Tdy,i,j (t) is the dynamic instantaneous undeformed chip thickness caused by tool vibration, which is expressed by Equation (8), and h Wdy,i,j (t) is the dynamic instantaneous undeformed chip thickness caused by workpiece self-vibration, which is expressed by Equation (9).

[0022]

[0023] h Tdy,i,j (t) = x T (t)sinφ i,j (t) + y T (t)cosφ i,j (t) (8)

[0024] h Wdy,i,j (t) = [x(t) - x(t - T)]sinφ i,j (t) + [y(t) - y(t - T)]cosφ i,j (t) (9)

[0025] In Equation (7), ω is the spindle speed, and φ p is the angular pitch between tool teeth, and φ p = 2π / N, where N is the number of tool teeth, and k β is the lag angle of the differential unit on the tool tooth; and k β = 2tanβ / D, where β is the tool helix angle and D is the tool diameter; in Equation (8), x T (t) is the vibration of the tool tip point in the X direction, and y T (t) is the vibration of the tool tip point in the Y direction, which is expressed by Equation (10); in Equation (9), x(t) - x(t - T) is the dynamic displacement of the workpiece in the X direction for the current tooth cycle and the previous tooth cycle, and y(t) - y(t - T) is the dynamic displacement of the workpiece in the Y direction for the current and previous tooth cycles;

[0026]

[0027] In Equation (10), f0 is the natural frequency of tool vibration, x0 is the amplitude of the tool tip in the X direction, and y0 is the amplitude of the tool tip in the Y direction;

[0028] Substituting Equation (10) into Equation (8), and substituting Equations (8) and (9) into Equation (6), the dynamic instantaneous undeformed chip thickness considering vibration is obtained, which is expressed by Equation (11).

[0029]

[0030] Substitute Equation (5) and Equation (11) into (3), and the instantaneous undeformed chip thickness considering vibration is obtained, expressed as Equation (12).

[0031]

[0032] Substitute Equation (12) and Equation (4) into Equation (2), and the instantaneous undeformed chip thickness considering vibration and tool wear effects is obtained, expressed as Equation (13).

[0033]

[0034] For the convenience of verifying the theoretical model, the shear force on the rake face considering vibration and tool wear effects in the physical space is transformed to the O-XYZ coordinate system; according to Equation (1), the shear force on the rake face considering vibration and tool wear effects in the O-XYZ coordinate system is expressed as Equation (14).

[0035]

[0036] where

[0037] Substitute Equation (13) into Equation (14), and Equation (15) is obtained:

[0038]

[0039] The specific process of Step ② is as follows.

[0040] During milling, in the dynamic evolution process of the flank wear width, there is a maximum elastic contact area VB between the flank of the tool and the machined surface of the workpiece. * , from the sharp state of the tool to the flank wear width reaching the maximum elastic contact area VB * before, that is, when 0 < VB(t) ≤ VB * , the contact mode between the flank of the tool and the machined surface of the workpiece is pure elastic contact; as the flank wear width of the tool gradually increases, on the basis of elastic contact, plastic flow contact begins to appear between the flank of the tool and the machined surface of the workpiece. At this time, the contact mode between the flank of the tool and the machined surface of the workpiece is the coexistence of elastic contact and plastic flow contact. This contact state between the flank of the tool and the machined surface of the workpiece will continue until the flank wear width VB(t) of the tool reaches the wear-out criterion VB, that is, the tool wear width VB * < VB(t) ≤ VB. During this process, as the tool wear width continuously increases, the contact area between the flank of the tool and the machined surface of the workpiece also continuously increases, and the width of the elastic contact area between the flank of the tool and the machined surface of the workpiece remains unchanged, with a size of VB. *, the width of the plastic flow contact zone between the machined surface of the workpiece and the flank face of the tool continuously increases, with a magnitude of VB P = VB(t) - VB * ;

[0041] Define VB P as the width of the plastic flow contact zone between the machined surface of the workpiece and the flank face of the tool, and define VB * as the maximum elastic contact zone width; during the machining process, when the flank wear width of the tool is greater than the maximum elastic contact zone width and before reaching the tool dulling standard, i.e., VB * < VB(t) < VB, the width of the elastic contact zone remains unchanged, and the plastic flow zone increases with the increase in the flank wear width of the tool; VB P is expressed as Equation (16),

[0042]

[0043] For the convenience of the milling force modeling research of the tool, in the space coordinate system, the tool is discretized along the axial direction into several differential elements, and one of the differential elements is extracted to analyze the frictional force acting on the flank face of the tool; the frictional force acting on the flank face of the tool during the machining process is represented by F w , which is composed of the normal frictional force F nw and the feed-direction frictional force F fw , and is expressed as Equation (17),

[0044] F w = F nw + F fw (17)

[0045] The frictional force on the flank face of the j-th tooth of the i-th differential element of the milling cutter is expressed as Equation (18),

[0046]

[0047] where, σ v (x) is the normal stress at a distance x from the cutting edge on the flank face, τ v (x) is the shear stress at a distance x from the cutting edge on the flank face, and VB(t) is the flank wear width of the tool; during the modeling process of the frictional force on the flank face considering the vibration and tool wear effects, the influence of vibration on the frictional force on the flank face is mainly reflected in the distribution of the extrusion stress in the contact area between the flank face of the tool and the machined surface of the workpiece, that is, the distribution of the normal stress σ v (x) and the shear stress τ v (x) in the contact area between the flank face of the tool and the machined surface of the workpiece;

[0048] In summary, through the above calculations, a method for predicting the flank wear width of a cutting tool based on the milling force at the machining site is proposed, which is used to accurately predict the flank wear width of the cutting tool during the machining of thin-walled parts;

[0049] The present invention provides a method for predicting the flank wear width of a cutting tool based on the milling force at the machining site, which has the following beneficial effects:

[0050] (1) Based on physical model modeling, it can better reveal the mapping relationship between the milling force and the flank wear width of the cutting tool during the machining process;

[0051] (2) Considering the influence of vibration and tool wear state on the milling force during the machining process, it is closer to the actual machining process, the prediction result of the milling force is more accurate, and the prediction of the tool wear width based on the milling force is also more accurate;

[0052] (3) The physical model has better generalization ability and can be applied to different machining scenarios and different machining parameters, with better versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly introduced below;

[0054] The drawings in the following description only relate to some embodiments of the present invention and do not limit the present invention;

[0055] Figure 1 is the step flow chart of the present invention;

[0056] Figure 2 is the schematic diagram of shear force analysis of the present invention;

[0057] Figure 3 is the schematic diagram of the instantaneous undeformed chip thickness considering vibration and tool wear effects of the present invention;

[0058] Figure 4 is the schematic diagram of the tool wear evolution process of the present invention;

[0059] Figure 5 is the schematic diagram of the flank friction force of the cutting tool of the present invention;

[0060] Figure 6 is the schematic diagram of cutting force analysis of the present invention;

[0061] Figure 7 is the flow chart of calculating the flank wear width of the cutting tool of the present invention;

[0062] Figure 8 is the comparison chart of milling force prediction and test results of the present invention;

[0063] Figure 9This is a comparison chart of the predicted flank wear width of the tool in the present invention and the test results. Detailed implementation manners

[0064] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. As Figure 1 shown, the present invention provides a method for predicting the flank wear width of a tool based on the milling force at the machining site, which is characterized in that it includes the following steps.

[0065] ① Establish a shear force prediction model considering vibration and tool flank wear effects.

[0066] In the space coordinate system, as Figure 2 shown, the tool is discretized into a number of differential elements along the axial direction. The shear force received by the jth tooth of the ith differential element on the milling cutter is expressed as Equation (1).

[0067]

[0068] In the formula, K tc , K rc and K ac are the tangential, radial, and axial shear force coefficients respectively, and K te , K re and K ae are the tangential, radial, and axial edge force coefficients respectively. h v,w,i,j (t) is the instantaneous undeformed chip thickness considering vibration and tool wear effects, as Figure 3 (d) shown, and is expressed by Equation (2).

[0069] h v,w,i,j (t) = h v,i,j (t) - h w,i,j (t) (2)

[0070] In the formula: h v,i,j (t) is the instantaneous undeformed cutting thickness considering vibration, as Figure 3 (b) shown, and is expressed by Equation (3); h w,i,j (t) is the influence of tool wear effect on the instantaneous undeformed cutting thickness, as Figure 3 (c) shown, and is expressed by Equation (4).

[0071] h v,i,j (t) = h sa,i,j (t) + h dy,i,j (t) (3)

[0072]

[0073] In Equation (3), h sa,i,j(t) is the static instantaneous undeformed chip thickness under ideal cutting conditions, as shown in Figure 3 (a), and is represented by Equation (5); h dy,i,j (t) is the dynamic instantaneous undeformed chip thickness considering vibration, and is represented by Equation (6),

[0074] h sa,i,j (t) = fsinφ i,j (t) (5)

[0075] h dy,i,j (t) = h Tdy,i,j (t) + h Wdy,i,j (t) (6)

[0076] In Equation (5), f is the feed per tooth, and φ i,j (t) is the instantaneous rotation angle of the i-th differential unit on the j-th tooth of the tool, and is represented by Equation (7). In Equation (6), h Tdy,i,j (t) is the dynamic instantaneous undeformed chip thickness caused by tool vibration, and is represented by Equation (8). h Wdy,i,j (t) is the dynamic instantaneous undeformed chip thickness caused by workpiece self-vibration, and is represented by Equation (9),

[0077]

[0078] h Tdy,i,j (t) = x T (t)sinφ i,j (t) + y T (t)cosφ i,j (t) (8)

[0079] h Wdy,i,j (t) = [x(t) - x(t - T)]sinφ i,j (t) + [y(t) - y(t - T)]cosφ i,j (t) (9)

[0080] In Equation (7), ω is the spindle speed, and φ p is the tool tooth space angle, and φ p = 2π / N, where N is the number of tool teeth, and k β is the lag angle of the differential unit on the tool tooth; and k β = 2tanβ / D, where β is the tool helix angle and D is the tool diameter. In Equation (8), x T (t) is the vibration of the tool tip point in the X direction, and y T(t) is the vibration of the tool tip point in the Y direction, which is represented by Equation (10); in Equation (9), x(t) - x(t - T) is the dynamic displacement of the workpiece in the X direction in the current tooth cycle and the previous tooth cycle, and y(t) - y(t - T) is the dynamic displacement of the workpiece in the Y direction in the current and previous tooth cycles;

[0081]

[0082] In Equation (10), f0 is the natural frequency of the tool vibration, x0 is the amplitude of the tool tip in the X direction, and y0 is the amplitude of the tool tip in the Y direction;

[0083] Substitute Equation (10) into Equation (8), and substitute Equations (8) and (9) into Equation (6), the dynamic instantaneous undeformed chip thickness considering vibration is obtained, which is expressed as Equation (11),

[0084]

[0085] Substitute Equations (5) and (11) into (3), the instantaneous undeformed cutting thickness considering vibration is obtained, which is expressed as Equation (12),

[0086]

[0087] Substitute Equations (12) and (4) into Equation (2), the instantaneous undeformed chip thickness considering vibration and tool wear effect is obtained, which is expressed as Equation (13),

[0088]

[0089] For the convenience of verifying the theoretical model, the shear force on the rake face considering vibration and tool wear effect in the physical space is transformed to the O-XYZ coordinate system; according to Equation (1), the shear force on the rake face considering vibration and tool wear effect in the O-XYZ coordinate system is expressed as Equation (14),

[0090]

[0091] In the formula

[0092] Substitute Equation (13) into Equation (14) to obtain Equation (15),

[0093]

[0094] ② Establish a friction force prediction model considering vibration and tool flank wear effect

[0095] As Figure 4 shown, during milling, there is a maximum elastic contact area VB between the tool flank and the machined surface of the workpiece during the dynamic evolution process of the flank wear width. *, from the sharp state of the cutting tool until the flank wear width reaches the maximum elastic contact area VB * before, that is, 0 < VB(t) ≤ VB * when, the contact mode between the flank of the cutting tool and the machined surface of the workpiece is pure elastic contact; as the flank wear width of the cutting tool gradually increases, on the basis of elastic contact, plastic flow contact begins to appear between the flank of the cutting tool and the machined surface of the workpiece. At this time, the contact mode between the flank of the cutting tool and the machined surface of the workpiece is the coexistence of elastic contact and plastic flow contact. This contact state between the flank of the cutting tool and the machined surface of the workpiece will continue until the wear width VB(t) of the flank of the cutting tool reaches the wear criterion VB, that is, the cutting tool wear width VB * < VB(t) ≤ VB. During this process, as the cutting tool wear width continuously increases, the contact area between the flank of the cutting tool and the machined surface of the workpiece also continuously increases. The width of the elastic contact area between the flank of the cutting tool and the machined surface of the workpiece remains unchanged, with a size of VB * , the width of the plastic flow contact area between the machined surface of the workpiece and the flank of the cutting tool continuously increases, with a size of VB P = VB(t) - VB * ;

[0096] Define VB P as the width of the plastic flow contact area between the machined surface of the workpiece and the flank of the cutting tool, and define VB * as the width of the maximum elastic contact area; during the machining process, when the flank wear width of the cutting tool is greater than the width of the maximum elastic contact area and before reaching the cutting tool wear criterion, that is, VB * < VB(t) < VB, the width of the elastic contact area remains unchanged, and the plastic flow area increases with the increase of the flank wear width of the cutting tool; VB P is expressed as Equation (16),

[0097]

[0098] For the convenience of the milling force modeling research of the cutting tool, in the space coordinate system, the cutting tool is discretized along the axial direction into several differential units, and one of the differential units is extracted to analyze the frictional force acting on the flank of the cutting tool; the frictional force acting on the flank of the cutting tool during the machining process is represented by F w , which is composed of the normal frictional force F nw and the feed-direction frictional force F fw , and is expressed as Equation (17),

[0099] F w = F nw + F fw (17)

[0100] The frictional force on the j-th tooth of the i-th differential unit of the milling cutter on the flank is expressed as Equation (18).

[0101]

[0102] Where, σ v (x) is the normal stress at a distance x from the cutting edge on the flank, τ v (x) is the shear stress at a distance x from the cutting edge on the flank, and VB(t) is the flank wear width of the tool; in the process of modeling the frictional force on the flank considering the vibration and tool wear effects, the influence of vibration on the frictional force on the flank is mainly reflected in the distribution of the extrusion stress in the contact area between the flank of the tool and the machined surface of the workpiece, that is, the distribution of the normal stress σ v (x) and the shear stress τ v (x) in the contact area between the flank of the tool and the machined surface of the workpiece;

[0103] When 0 < VB(t) < VB * , the contact between the machined surface of the workpiece and the flank of the tool is a pure elastic contact. σ v (x) and τ v (x) in Equation (18) are expressed as Equation (19).

[0104]

[0105] Where: σ0 is the constant value of the normal stress, τ0 is the constant value of the shear stress, VB(t) is the flank wear width, x is the distance between the point in the worn area on the flank and the cutting edge, μ is the friction coefficient between the flank of the tool and the machined surface of the workpiece, and λ(x) is the vibration compensation factor, and λ(x) = (x - VB(t)) 2 ;

[0106] For the convenience of subsequent model calculation, according to the stress distribution in the contact area between the flank of the tool and the machined surface of the workpiece in Equation (19), the frictional force on the flank of the j-th tooth of the i-th differential unit of the milling cutter in Equation (18) is further expressed as Equation (20).

[0107]

[0108] Substituting Equation (19) into Equation (20) gives Equation (21).

[0109]

[0110] Transform the frictional force on the flank of the tool in the physical space to the O-XYZ coordinate system; then when 0 < VB(t) ≤ VB * , the frictional force on the flank of the j-th tooth of the milling cutter is expressed as Equation (22).

[0111]

[0112] In the formula

[0113] Substituting Equation (21) into Equation (22) gives Equation (23).

[0114]

[0115] Equation (23) is the prediction model of the flank friction force of the tool considering the vibration and flank wear effect of the tool when 0 < VB(t) ≤ VB * When considering the vibration and flank wear effect of the tool, the prediction model of the flank friction force of the tool when 0 < VB(t) ≤ VB

[0116] When VB * When VB < VB(t) ≤ VB, the contact between the machined surface of the workpiece and the flank of the tool is a combination of elastic contact and plastic flow contact. σ v (x) and τ v (x) are expressed as Equation (24).

[0117]

[0118] The meanings of the symbols in Equation (24) are the same as those in Equation (19).

[0119] For the convenience of subsequent model calculation, according to the stress distribution in the contact area between the flank of the tool and the machined surface of the workpiece in Equation (24), the flank friction force on the i-th differential unit of the j-th tooth of the milling cutter in Equation (18) is further expressed as Equation (25).

[0120]

[0121] Substituting Equation (24) into Equation (25) gives Equation (26).

[0122]

[0123] Converting the flank friction force of the tool in the physical space to the O-XYZ coordinate system, then when VB * When VB < VB(t) ≤ VB, the flank friction force of the j-th tooth of the milling cutter is expressed as Equation (27).

[0124]

[0125] Among them,

[0126] Substituting Equation (26) into Equation (27) gives Equation (28).

[0127]

[0128] Equation (28) is VB *When VB(t) ≤ VB, a prediction model for the friction force on the flank face of the tool considering vibration and flank wear effects of the tool;

[0129] ③ Establish a prediction model for milling force considering vibration and flank wear effects of the tool

[0130] As Figure 6 shown, the time-varying milling force of the j-th tooth on the milling cutter considering vibration and tool wear effects is expressed by Equation (29),

[0131]

[0132] When 0 < VB(t) ≤ VB * at this time, substituting Equations (15) and (23) into Equation (29), the milling force model considering vibration and tool wear effects in the pure elastic contact state between the flank face of the tool and the machined surface of the workpiece is obtained; when VB * < VB(t) ≤ VB, substituting Equations (15) and (28) into Equation (29), the milling force model considering vibration and tool wear effects in the state where elastic contact and plastic flow contact coexist between the flank face of the tool and the machined surface of the workpiece is obtained.

[0133] ④ Construct a mapping relationship model between milling force and flank wear width of the tool

[0134] According to the milling force model considering vibration and tool wear effects, the mapping relationship between the flank wear width of the tool and the milling force is obtained, expressed as,

[0135] VB(t) = f1(F(t)) (30)

[0136] VB(t) = f2(F(t)) (31)

[0137] Equation (30) represents the mapping relationship between the flank wear width of the tool and the milling force when 0 < VB(t) ≤ VB * at this time; Equation (31) represents the mapping relationship between the flank wear width of the tool and the milling force when VB * < VB(t) ≤ VB;

[0138] The present invention uses a cutting test of a titanium alloy thin-walled part to verify the feasibility and practicality of the present invention; the following uses a specific example to illustrate the effect of the present invention;

[0139] The test uses Ti-6Al-4V, and the material parameters are Young's modulus of 108 GPa, Poisson's ratio of 0.34, and material density of 4500 kg / m 3, the size of the test plate was 105×20×5 mm; a two-flute carbide end mill with a diameter of 8 mm, a length of 50 mm, and a helix angle of 30° was selected; all tests were carried out on a three-axis milling center (VMC-850E), and the dynamic milling force signal was measured by a dynamometer (Kistler 9257B); in addition, a super-depth-of-field microscope (VH X-2000) was used to observe the tool wear state;

[0140] The calculation process of the proposed method in this time is as Figure 7 shown. During the calculation process of the flank wear width of the tool, the parameters that need to be calibrated according to the tests are: the tangential, radial, and axial shear force coefficients K tc , K rc , K ac and the edge force coefficient K te , K re , K ae ; the natural frequency f0 of the tool vibration, the amplitude x0 of the tool tip in the X direction, the amplitude y0 of the tool tip in the Y direction; the maximum elastic contact zone width VB * between the flank of the tool and the machined surface of the workpiece, the constant value σ0 of the normal stress and the constant value τ0 of the shear stress between the flank of the tool and the machined surface of the workpiece;

[0141] The milling force prediction results of the proposed method under the determined flank wear width are as Figure 8 shown; Figure 8 It shows that the average errors of the milling force prediction results in the X and Y directions are 3.5% and 5.75% respectively, indicating that the milling force prediction under the determined flank wear width is relatively accurate;

[0142] The flank wear width prediction results of the proposed method based on the milling force are as Figure 9 shown; Figure 9 It shows that the prediction errors of the flank wear width of the tool based on the milling force in the X and Y directions are 8.7% and 8% respectively, indicating that the flank wear width prediction based on the milling force is relatively accurate;

[0143] This embodiment does not make any formal restrictions on the shape, material, structure, etc. of the present invention. Any simple modifications, equivalent changes, and decorations made to the above embodiments based on the technical essence of the present invention all belong to the protection scope of the technical solution of the present invention.

Claims

1. A method for predicting tool flank wear width based on milling force at a machining site, characterized in that: The following steps are included: ① Establish a shear force prediction model that takes into account the effects of vibration and tool flank wear; ② Establish a friction force prediction model that takes into account the effects of vibration and tool flank wear; ③ Establish a milling force prediction model that considers the effects of vibration and tool flank wear; ④Construct a mapping relationship model between milling force and tool flank wear width.

2. The method for predicting tool flank wear width based on milling force at a machining site according to claim 1, characterized in that: The shear force prediction model considering the vibration and tool flank wear effects is established in the following specific process: In the spatial coordinate system, the tool is discretized into several differential units along the axial direction. The shear force on the jth tooth of the i-th differential unit on the milling cutter is expressed as formula (1): In the formula, K tc ,K rc and K ac are the tangential, radial and axial shear force coefficients, K te ,K re and K ae are the tangential, radial and axial edge force coefficients, respectively, and h v,w,i,j (t) is the instantaneous undeformed chip thickness considering the vibration and tool wear effects, expressed by equation (2), h v,w,i,j (t)=h v,i,j (t)-h w,i,j (t) (2) In the formula, h v,i,j (t) is the instantaneous undeformed cutting thickness considering vibration, expressed by formula (3); h w,i,j (t) is the influence of tool wear effect on instantaneous undeformed cutting thickness, expressed by formula (4), h v,i,j (t)=h sa,i,j (t)+h dy,i,j (t) (3) In formula (3), h as,i,j (t) is the static instantaneous undeformed chip thickness under ideal cutting conditions, expressed by formula (5); h dy,i,j (t) is the dynamic instantaneous undeformed chip thickness considering vibration, which is expressed by formula (6): h sa,i,j (t)=fsinφ i,j (t) (5) h dy,i,j (t)=h Tdy,i,j (t)+h Wdy,i,j (t) (6) In formula (5), f is the feed per tooth, φ i,j (t) is the instantaneous rotation angle of the i-th differential unit on the j-th tooth of the tool, which is expressed by equation (7), while in equation (6), h Tdy,i,j (t) is the dynamic instantaneous undeformed chip thickness caused by tool vibration, expressed by equation (8), h Wdy,i,j (t) is the dynamic instantaneous undeformed chip thickness caused by the vibration of the workpiece itself, expressed by formula (9), h Tdy,i,j (t)=x T (t)sinφ i,j (t)+y T (t)cosφ i,j (t) (8) h Wdy,i,j (t)=[x(t)-x(t-T)]sinφ i,j (t)+[y(t)-y(t-T)]cosφ i,j (t) (9) In formula (7), ω is the spindle speed, φ p is the tool tooth angle, and φ p =2π / N, N is the number of tool teeth, k β is the lag angle of the differential unit on the cutter tooth, and k β =2tanβ / D, where β is the tool helix angle and D is the tool diameter; in formula (8), x T (t) is the vibration of the tool tip in the X direction, y T (t) is the vibration of the tool tip in the Y direction, which is expressed by formula (10); in formula (9), x(t)-x(tT) is the dynamic displacement of the current tooth cycle and the previous tooth cycle in the X direction of the workpiece, and y(t)-y(tT) is the dynamic displacement of the current and previous tooth cycles in the Y direction of the workpiece; In formula (10), f0 is the natural frequency of tool vibration, x0 is the amplitude of tool tip in the X direction, and y0 is the amplitude of tool tip in the Y direction; Substituting equation (10) into equation (8), and substituting equation (8) and equation (9) into equation (6), we can obtain the dynamic instantaneous undeformed chip thickness considering vibration, which is expressed as equation (11): Substituting equations (5) and (11) into equation (3), we can obtain the instantaneous undeformed cutting thickness considering vibration, which is expressed as equation (12): Substituting equations (12) and (4) into equation (2), we can obtain the instantaneous undeformed chip thickness h considering the effects of vibration and tool wear: v,w,i,j (t), expressed as formula (13), In order to verify the theoretical model, the rake face shear force considering the vibration and tool wear effects in the physical space is converted to the O-XYZ coordinate system. According to formula (1), the rake face shear force considering the vibration and tool wear effects in the O-XYZ coordinate system is expressed as formula (14): In the formula, Substituting formula (13) into formula (14) yields formula (15), 3. The method for predicting tool flank wear width based on milling force at a machining site according to claim 1, characterized in that: The friction force prediction model considering the vibration and tool flank wear effects is established in the following specific process: During milling, in the dynamic evolution process of the flank wear width, there exists a maximum elastic contact area VB between the flank of the tool and the machined surface of the workpiece. * Before the tool wears from a sharp state to a flank wear width reaching the maximum elastic contact area VB * , that is, when 0 < VB(t) ≤ VB * , the contact mode between the flank of the tool and the machined surface of the workpiece is pure elastic contact; as the flank wear width of the tool gradually increases, on the basis of elastic contact, plastic flow contact begins to appear between the flank of the tool and the machined surface of the workpiece. At this time, the contact mode between the flank of the tool and the machined surface of the workpiece is the coexistence of elastic contact and plastic flow contact. This contact state between the flank of the tool and the machined surface of the workpiece will continue until the flank wear width VB(t) of the tool reaches the wear criterion VB, that is, the tool wear width VB * < VB(t) ≤ VB. During this process, as the tool wear width continuously increases, the contact area between the flank of the tool and the machined surface of the workpiece also continuously increases. The width of the elastic contact area between the flank of the tool and the machined surface of the workpiece remains unchanged, with a size of VB * , and the width of the plastic flow contact area between the machined surface of the workpiece and the flank of the tool continuously increases, with a size of VB P = VB(t) - VB * ; Define VB P as the width of the plastic flow contact zone between the machined surface of the workpiece and the flank face of the cutting tool, and define VB * as the width of the maximum elastic contact zone; during the machining process, when the flank wear width of the cutting tool is greater than the width of the maximum elastic contact zone and before reaching the tool wear criterion, i.e., VB * < VB(t) < VB, the width of the elastic contact zone remains unchanged, and the plastic flow zone increases with the increase in the flank wear width of the cutting tool; VB P is expressed as Equation (16), In order to facilitate the research on the milling force modeling of the tool, the tool is discretized into several differential units along the axial direction in the spatial coordinate system, and one of the differential units is extracted to analyze the friction force acting on the tool back face; the friction force acting on the tool back face during the machining process is expressed by F w Indicated by the normal friction force F nw and the feed friction F fw Composition, expressed as formula (17), F w =F nw +F fw (17) The friction force on the jth tooth on the ith differential unit of the milling cutter axial direction is expressed as formula (18): Among them, σ v (x) is the normal stress on the back face at a distance x from the cutting edge, τ v (x) is the shear stress on the flank at a distance x from the cutting edge, and VB(t) is the wear width of the tool flank. In the process of modeling the flank friction force considering the vibration and tool wear effects, the influence of vibration on the flank friction force is mainly reflected in the extrusion stress distribution in the contact area between the tool flank and the machined surface of the workpiece, that is, the flank normal stress σ v (x) and the shear stress τ on the flank v (x) Distribution of contact area between tool flank and machined workpiece surface; When 0 <VB(t)<VB * When , the workpiece machined surface and the tool back face are in pure elastic contact, and σ in formula (18) v (x) and τ v (x) is expressed as formula (19), Where: σ0 is the constant value of normal stress, τ0 is the constant value of shear stress, VB(t) is the wear width of the flank, x is the distance between the point in the wear area on the flank and the cutting edge, μ is the friction coefficient between the flank of the tool and the machined surface of the workpiece, λ(x) is the vibration compensation factor, and λ(x)=(x-VB(t)) 2 ; In order to facilitate the subsequent model calculation, according to the stress distribution of the contact area between the tool flank and the machined surface of the workpiece in formula (19), the friction force on the flank of the i-th differential unit of the j-th tooth on the milling cutter in formula (18) is further expressed as formula (20): Substituting equation (19) into equation (20) yields equation (21), Convert the friction force of the tool back face in the physical space to the O-XYZ coordinate system; then 0 <VB(t)≤VB * When , the friction force on the jth tooth flank of the milling cutter is expressed as formula (22): In the formula Substituting equation (21) into equation (22) yields equation (23), Formula (23) is 0 <VB(t)≤VB * When , the tool flank friction force prediction model; When VB * <When VB(t) ≤ VB, the contact between the machined surface of the workpiece and the flank face of the tool is a combination of elastic contact and plastic flow contact. σ v (x) and τ v (x) are expressed as Equation (24), The meanings of symbols in formula (24) are the same as those in formula (19); To facilitate subsequent model calculations, according to the stress distribution in the contact area between the tool flank and the machined surface of the workpiece in equation (24), the flank friction force on the i-th differential unit of the j-th tooth on the milling cutter in equation (18) is further expressed as equation (25): Substituting equation (24) into equation (25) yields equation (26), Convert the friction force on the flank face of the cutting tool in the physical space to the O-XYZ coordinate system, then VB * When <VB(t)≤VB, the friction force on the flank face of the j-th tooth of the milling cutter is expressed by Equation (27). in Substituting formula (26) into formula (27) we get formula (28): Equation (28) is VB * When <VB(t) ≤ VB, the prediction model of the friction force on the flank face of the cutting tool.

4. The method for predicting tool flank wear width based on milling force at a machining site according to claim 1, characterized in that: The milling force prediction model considering the effects of vibration and tool flank wear is established in the following specific process: The time-varying milling force of the jth tooth on the milling cutter considering the effects of vibration and tool wear is expressed by equation (29): When \(0 < V_{B}(t)\leq V_{B}\) * , substituting Eqs. (15) and (23) into Eq. (29), the milling force model considering vibration and tool wear effects under the pure elastic contact state between the flank face of the tool and the machined surface of the workpiece is obtained; when \(V_{B}\) * < V_{B}(t)\leq V_{B}\), substituting Eqs. (15) and (28) into Eq. (29), the milling force model considering vibration and tool wear effects under the state where elastic contact and plastic flow contact coexist between the flank face of the tool and the machined surface of the workpiece is obtained.

5. The method for predicting tool flank wear width based on milling force at a machining site according to claim 1, characterized in that: The mapping relationship model between the milling force and the tool flank wear width is constructed in the following specific process: According to the milling force model considering the effects of vibration and tool wear, the mapping relationship between the tool flank wear width and the milling force is obtained, which is expressed as: VB(t)=f1(F(t)) (30) VB(t)=f2(F(t)) (31) Equation (30) represents the mapping relationship between the flank wear width of the tool and the milling force when 0 < VB(t) ≤ VB * ; Equation (31) represents the mapping relationship between the flank wear width of the tool and the milling force when VB * < VB(t) ≤ VB

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