Identification and verification method of time-lapse variability of surface topography processed by end mill under vibration conditions

Abstract

The method for identifying and verifying the time-lapse variability of the surface morphology processed by an end mill under vibration conditions belongs to the field of milling cutter processing technology. It includes designing an experimental plan for milling vibration and surface morphology of titanium alloy processed by an end mill; designing a method for constructing a distribution sequence of surface morphology processed by an end mill under vibration conditions; establishing a time-lapse variability solution model for the surface morphology processed under the influence of vibration; step 4, designing an efficient method for identifying the distribution characteristics of the surface morphology processed by milling; designing a method for analyzing and experimentally verifying the time-lapse variability response of the surface morphology processed; based on the characterization of the existing surface morphology distribution characteristics of milling, the instantaneous cutting behavior of each tooth has the same variation characteristics, ignoring the variability and complexity of the processing process, and proposing a method for solving the time-lapse variability of the surface morphology processed by milling, revealing the influence of cutting parameters, tooth errors and milling vibration on the surface morphology processed.

Description

Technical Field

[0001] The invention relates to a method for identifying and verifying time-shift variability of surface topography processed by an end mill under vibration conditions, and belongs to the technical field of milling cutter processing. Background Art

[0002] Milling surface morphology is the key information reflecting the machining status. Existing methods for the formation of milling surface morphology mainly focus on the multi-tooth equal pitch cutting of the milling cutter, ignoring the influence of tooth error on the distribution of machined surface morphology. To this end, an experiment of efficient milling of titanium alloy was carried out using an integral end mill, and the milling vibration signal was extracted from the machining process; using the milling vibration at different positions corresponding to different periods, a method for analyzing the time-frequency characteristic parameters of milling vibration and machined surface morphology was proposed to characterize the variability of milling surface morphology distribution; using the milling surface morphology, a sequence of milling surface morphology characteristic parameters was constructed to reveal the influence of tooth error and vibration on the machined surface morphology. Using the instantaneous cutting posture of the milling cutter, a method for solving the machined surface morphology was constructed to reveal the formation mechanism of the machined surface morphology.

[0003] In the characterization of the distribution characteristics of the existing milling surface morphology, the instantaneous cutting behavior of each cutter tooth has the same change characteristics, which ignores the variability and complexity of the machining process. Therefore, it is urgent to propose a new method for identifying and verifying the time-lapse variability of the surface morphology of end mill machining under vibration conditions to solve the above technical problems. Summary of the invention

[0004] The purpose of the research and development of the present invention is to solve the problem that the instantaneous cutting behavior of each tooth has the same change characteristics in the characterization of the distribution characteristics of the existing milling surface morphology, and ignores the variability and complexity of the processing process. The present invention adopts the time-frequency analysis method of the characteristic curve of the processing surface morphology to characterize the distribution characteristics of the processing surface morphology. A method for solving the time-shift variability of the milling surface morphology is proposed to reveal the influence characteristics of cutting parameters, tooth errors and milling vibrations on the processing surface morphology. The response characteristics of the time-shift variability of the surface morphology of efficient milling of aviation components are studied and verified. A brief overview of the present invention is given below to provide a basic understanding of certain aspects of the present invention. It should be understood that this overview is not an exhaustive overview of the present invention. It is not intended to determine the key or important parts of the present invention, nor is it intended to limit the scope of the present invention.

[0005] The technical solution of the present invention:

[0006] The identification and verification method of time-lapse variability of surface topography processed by end mill under vibration conditions includes:

[0007] Step 1: Design an experimental plan for milling vibration and surface morphology of titanium alloy by end mill:

[0008] An experiment on efficient milling of titanium alloy was conducted using an integral end mill, and the milling vibration signal was extracted from the machining process. Using the milling vibrations at different positions at different times, a method for analyzing the time-frequency characteristic parameters of milling vibration and machined surface morphology was proposed to characterize the variability of milling surface morphology distribution.

[0009] Step 2: Design a method for constructing a sequence of surface topography distribution of end mill machining under vibration conditions:

[0010] By using the milling surface topography, the characteristic parameter sequence of the milling surface topography is constructed to reveal the influence of the cutter tooth error and vibration on the machined surface topography.

[0011] Step 3: Establish a time-lapse multi-variability solution model for the machining surface morphology under the influence of vibration:

[0012] Using the instantaneous cutting posture of the milling cutter, a method for calculating the machined surface topography is constructed to reveal the formation mechanism of the machined surface topography.

[0013] Step 4: Design an efficient milling surface topography distribution characteristics identification method:

[0014] The time-frequency analysis method of the machined surface morphology characteristic curve is used to characterize the distribution characteristics of the machined surface morphology;

[0015] Step 5: Design the time-lapse multi-variable response analysis and experimental verification method of the processed surface morphology:

[0016] A method for solving the time-lapse variability of milling surface topography is proposed to reveal the influence of cutting parameters, tooth error and milling vibration on the machined surface topography; the response characteristics of the time-lapse variability of the surface topography of efficient milling of aviation components are studied and verified.

[0017] Preferably: Step 1 comprises:

[0018] Before the experiment, the axial error and radial error of each tooth of the milling cutter were detected by a tool measuring instrument to identify the corresponding tool tip point. s ij ;

[0019] In the experiment, the transient signal test and analysis system was used to obtain the milling vibration displacement signal;

[0020] After the experiment is completed, a white light interferometer is used to detect the surface morphology of the component processing;

[0021] Finally, the moment when the milling cutter enters the workpiece is calculated. t 0, and the measurement length of the white light interferometer Corresponding milling cutter cutting time ,as follows:

[0022] (1)

[0023] (2)

[0024] in, is the spindle speed; is the workpiece coordinate system, The milling cutter corresponding to the start time of vibration signal acquisition The position of the axis, For machining surface morphology The sampling position of the axis, is the sampling interval, for The corresponding milling cutter cutting time, for The corresponding milling cutter cutting time, is the maximum radial radius of the milling cutter teeth, is the cutting feed speed.

[0025] Preferably: the step 2 comprises:

[0026] According to the axial error of the cutter teeth From small to large, obtain the characteristic curve of the machined surface morphology along the milling cutter feed direction within the tooth axial error distribution range, where the position of the morphology curve satisfies:

[0027] (3)

[0028] in, is the measurement height of the white light interferometer, The milling cutter corresponding to the start time of vibration signal acquisition The position of the axis, It is the sampling position of the surface topography along the cutting depth direction;

[0029] The root mean square of the surface topography characteristic curve processed at different positions along the milling cutter feed direction , Kurtosis and main frequency , and the RMS of milling vibration in the corresponding period , Kurtosis and main frequency , construct the distribution sequence of machined surface morphology characteristics and milling vibration characteristics in different tooth axial error distribution intervals, and characterize the distribution sequence of machined surface morphology under the influence of milling vibration and tooth error, as follows:

[0030] (4)

[0031] (5)

[0032] in, They are the kurtosis, RMS value and main frequency sequence of the machined surface morphology in different tooth axial error distribution ranges; They are the RMS value, kurtosis and main frequency sequence of milling vibration respectively.

[0033] Preferably: Step 3 comprises:

[0034] According to the tooth error and milling vibration conditions, the instantaneous cutting posture of the solid carbide end mill is established. The cutting coordinate system, and Coordinate system of milling cutter without vibration;

[0035] In the cutter tooth coordinate system, the cutter tooth Cutting edge equation for:

[0036] (6)

[0037] in ， is the blade tooth coordinate system, The tip of the blade The rotation center of Axis through origin And point to point, Axis and parallel, It is the lag angle of any point of the cutting edge relative to the tool tip;

[0038] The relationship between the cutting coordinate system and the workpiece coordinate system is:

[0039] (7)

[0040] and Axis relative to Instantaneous inclination of the axis and for:

[0041] (8)

[0042] in, is the milling cutter coordinate system The instantaneous position angle deviation between the axis and the workpiece coordinate system; is the tooth coordinate system The instantaneous position angle offset of the axis and workpiece coordinate system is as follows:

[0043] (9)

[0044] and Axis relative to Instantaneous position angle of the shaft ,as follows:

[0045] (10)

[0046] (11)

[0047] (12)

[0048] From equations (6) to (12), using the trajectory of any point on the cutting edge of the cutter tooth, the equation of the tooth cutting transition surface under the influence of the cutter tooth error and milling vibration is obtained as follows:

[0049] (13)

[0050] in, Cutting teeth i The cut-in and cut-out moments;

[0051] The relationship between the workpiece coordinate system and the cutter tooth coordinate system is:

[0052] (14)

[0053] in, R 1 is the rotation matrix of the cutting coordinate system and the milling cutter coordinate system without vibration, R 2. R 3 is the rotation matrix between the milling cutter coordinate system and the milling cutter coordinate system without vibration, R 4 is the rotation matrix of the milling cutter coordinate system and the tooth coordinate system; T 1 is the translation matrix between the workpiece coordinate system and the cutting coordinate system, T 2 is the translation matrix between the milling cutter coordinate system and the milling cutter coordinate system without vibration, T 3 is the translation matrix of the milling cutter coordinate system and the tooth coordinate system; the above matrix can be obtained by Figure 4 Determined by equations (7) to (12);

[0054] for The trajectory of a point;

[0055] (15)

[0056] for The trajectory of a point;

[0057] (16)

[0058] for The trajectory of a point;

[0059] (17)

[0060] The upper and lower boundaries of the trajectory of any point on the cutting edge participating in cutting within time are:

[0061] (18)

[0062] in, is the trajectory equation of tool tip point;

[0063] From formula (13), the intersection line of any adjacent transition surfaces can be obtained as:

[0064] (19)

[0065] Using equations (6) to (19), we can solve the cutting motion trajectory of each reference point of the cutting edge of the cutter and the intersection of other cutting transition surfaces of the cutter teeth to extract y Towards the minimum intersection point, identify the residual cutting transition surface of the cutter teeth and obtain the distribution of the machined surface morphology;

[0066] On the workpiece xoy In the coordinate system Arbitrary point establishment and workpiece coordinate system y Axis parallel lines L 1. Straight line L 1. Traverse from the machined surface to the end point of the machined surface to obtain the intersection point with the instantaneous cutting transition surface of the milling cutter teeth;

[0067] straight line L The intersection of 1 and each tooth trajectory is:

[0068] (20)

[0069] Each intersection point is based on y The point set sequence with coordinate values ​​from small to large is:

[0070] (twenty one)

[0071] According to formula (21), when the straight line Traverse from the starting point of the machined surface to the end point of the machined surface and obtain y The sequence of intersection points toward the minimum value is:

[0072] (twenty two)

[0073] According to formula (22), the milling surface morphology is established for:

[0074] (twenty three).

[0075] Preferably: Step 5 comprises:

[0076] Step 1: Input different cutting process plans;

[0077] Step 2, solving the instantaneous cutting posture of milling vibration;

[0078] Step 3: Process the surface solution model to identify the influencing characteristics of different cutting process solutions;

[0079] Step 4: Compare the correlation of distribution characteristics of different cutting process solutions;

[0080] Step 5, solving the comparison of distribution characteristics of the processed surface morphology;

[0081] Step six: Comparison of surface morphology distribution characteristics of experimental processing.

[0082] The present invention has the following beneficial effects:

[0083] 1. In the process of high-efficiency milling of titanium alloy by end mills, the instantaneous contact relationship between the milling cutter teeth and the workpiece is constantly changing due to the influence of milling vibration, cutter tooth error and cutting parameters, and the distribution characteristics of the milling surface morphology are complex and variable. The existing model method cannot accurately analyze the influence characteristics of milling vibration, cutter tooth error and cutting parameters on the milling surface morphology, and the factors affecting the variability of the milling surface morphology need to be revealed;

[0084] 2. The present invention uses an integral end mill to conduct an experiment on efficient milling of titanium alloy, extracting milling vibration signals from the machining process; utilizing milling vibrations at different positions corresponding to different time periods, a method for analyzing time-frequency characteristic parameters of milling vibration and machined surface morphology is proposed to characterize the variability of the distribution of milled surface morphology; utilizing the milled surface morphology, a sequence of milling surface morphology characteristic parameters is constructed to reveal the influence of tooth error and vibration on the machined surface morphology. Using the instantaneous cutting posture of the milling cutter, a method for solving the machined surface morphology is constructed to reveal the formation mechanism of the machined surface morphology. A method for time-frequency analysis of the characteristic curve of machined surface morphology is used to characterize the distribution characteristics of the machined surface morphology. A method for solving the time-shift variability of milled surface morphology is proposed to reveal the influence of cutting parameters, tooth error and milling vibration on the machined surface morphology. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 Schematic diagram of the structure of the end mill tooth structure of the present invention, wherein (a) is a front view of the end mill tooth structure, and (b) is a bottom view of the end mill tooth structure;

[0086] Figure 2 This is a graph showing the milling vibration and machined surface topography experimental results of the present invention;

[0087] Figure 3 It is a machined surface topography diagram within the distribution range of the axial error of the cutter teeth of the present invention;

[0088] Figure 4 The time-frequency characteristic change characteristic diagram of the milling vibration and the processed surface topography of the present invention, wherein (a) is the root mean square value change characteristic diagram, (b) is the kurtosis change characteristic diagram, and (c) is the main frequency change characteristic diagram;

[0089] Figure 5 It is the instantaneous cutting posture diagram of the knife of the present invention;

[0090] Figure 6 It is a diagram of the method for solving the milling surface topography of the present invention;

[0091] Figure 7 The present invention x 3-position machining surface topography;

[0092] Figure 8 The processing surface morphology characteristic curve distribution characteristic diagram of the present invention, wherein (a) is the root mean square value change characteristic diagram, (b) is the kurtosis change characteristic diagram, and (c) is the main frequency change characteristic diagram;

[0093] Fig. 9 3 are the machined surface morphology diagrams under the influence of different factors of the present invention, wherein (a) is the influence diagram of down milling and cutting parameters, (b) is the influence diagram of cutter tooth radial error, (c) is the influence diagram of cutter tooth axial error, and (d) is the influence diagram of milling vibration;

[0094] Fig.10 It is a time-frequency distribution diagram of the characteristic curve of the machined surface morphology under the influence of various factors of the present invention, wherein (a) is a root mean square value diagram of the machined surface morphology, (b) is a kurtosis diagram of the machined surface morphology, and (c) is a main frequency diagram of the machined surface morphology;

[0095] Fig.11 It is a flow chart of the method for identifying the time-lapse variability of the surface morphology of milling titanium alloy processing of the present invention;

[0096] Fig.12 It is a vibration signal and shape detection result diagram of the present invention;

[0097] Fig.13 It is a topography diagram of the machined surface under the conditions of the cutter tooth error and milling vibration of the present invention;

[0098] Fig.14 3 are the machined surface morphology diagrams under the influence of different factors of the present invention, wherein (a) is the influence diagram of down milling and cutting parameters, (b) is the influence diagram of cutter tooth radial error, (c) is the influence diagram of cutter tooth axial error, and (d) is the influence diagram of milling vibration;

[0099] Fig.15 It is a time-frequency distribution characteristic diagram of the characteristic curve of the machined surface morphology under the influence of various factors of the present invention, wherein (a) is a root mean square value diagram of the machined surface morphology, (b) is a kurtosis diagram of the machined surface morphology, and (c) is a main frequency diagram of the machined surface morphology;

[0100] Fig.16 It is a characteristic diagram of the time-shift variability of milling surface topography under different influencing factors of the present invention;

[0101] Fig.17 is a correlation diagram of the milling vibration and the distribution characteristics of the machined surface topography of the present invention;

[0102] Fig.18 It is a time-frequency characteristic diagram of the milling surface morphology of the present invention, wherein (a) is a root mean square value diagram of the machined surface morphology, (b) is a kurtosis diagram of the machined surface morphology, and (c) is a main frequency diagram of the machined surface morphology;

[0103] Fig.19 It is a time-frequency characteristic diagram of the milling surface morphology of the present invention, wherein (a) is a root mean square value diagram of the machined surface morphology, (b) is a kurtosis diagram of the machined surface morphology, and (c) is a main frequency diagram of the machined surface morphology; DETAILED DESCRIPTION

[0104] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is described below by the specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0105] Specific implementation method 1: Combination Figure 1-Figure 19 The present embodiment is described. The method for identifying and verifying the time-lapse variability of the surface topography processed by an end mill under vibration conditions in the present embodiment includes:

[0106] Step 1: Design an experimental plan for milling vibration and surface morphology of titanium alloy by end mill:

[0107] An experiment on efficient milling of titanium alloy was conducted using an integral end mill, and the milling vibration signal was extracted from the machining process. Using the milling vibrations at different positions at different times, a method for analyzing the time-frequency characteristic parameters of milling vibration and machined surface morphology was proposed to characterize the variability of milling surface morphology distribution.

[0108] Step 2: Design a method for constructing a sequence of surface topography distribution of end mill machining under vibration conditions:

[0109] By using the milling surface topography, the characteristic parameter sequence of the milling surface topography is constructed to reveal the influence of the cutter tooth error and vibration on the machined surface topography.

[0110] Step 3: Establish a time-lapse multi-variability solution model for the machining surface morphology under the influence of vibration:

[0111] Using the instantaneous cutting posture of the milling cutter, a method for calculating the machined surface topography is constructed to reveal the formation mechanism of the machined surface topography.

[0112] Step 4: Design an efficient milling surface topography distribution characteristics identification method:

[0113] The time-frequency analysis method of the machined surface morphology characteristic curve is used to characterize the distribution characteristics of the machined surface morphology;

[0114] Step 5: Design the time-lapse multi-variable response analysis and experimental verification method of the processed surface morphology:

[0115] A method for solving the time-lapse variability of milling surface topography is proposed to reveal the influence of cutting parameters, tooth error and milling vibration on the machined surface topography; the response characteristics of the time-lapse variability of the surface topography of efficient milling of aviation components are studied and verified.

[0116] The step 1 comprises:

[0117] In order to reveal the surface morphology distribution characteristics of aviation components processed by efficient milling under the influence of cutter tooth error and milling vibration, a solid carbide coated TiCN end mill was used to dry and down mill titanium alloy aviation components, such as Figure 1 The machine tool is a VDL-1000E three-axis milling machining center; the milling cutter has a diameter of 20 mm, 5 teeth, and a helix angle of 45°; the aviation component material is TC4, and the size is 200×100×25 mm.

[0118] Figure 1 middle, n is the spindle speed; D is the diameter of the milling cutter shank, l 1 is the total length of the milling cutter, l 2 is the overhang of the milling cutter, l 3 is the axial length of the cutting edge, β is the cutting edge helix angle; s zmin The lowest tooth tip point in the milling cutter axial direction. s zmax The highest tooth tip point in the milling cutter axis. s rmax It is the cutting edge point of the cutter tooth with the largest turning radius of the milling cutter; o d - x d y d z dis the milling cutter coordinate system, o d for s zmin The rotation center of x d Axis and s rmax The radial parallel, z d The axis is the rotary axis of the milling cutter; s ij is the tip of the milling cutter tooth, r ij for s ij The radius of gyration, i The numbers of the teeth are arranged in sequence in the opposite direction of the milling cutter speed. j The cutter tooth numbers are sorted from small to large according to the cutter tooth axial error. s 11 For along z d The lowest tooth tip on the shaft s zmin ; o i -x i y i z i is the blade tooth coordinate system, o i The tip of the blade s ij The rotation center of x i Axis through origin o i And point to s ij point, z i Axis and z d parallel, ζ ij It is the lag angle of any point of the cutting edge relative to the tool tip; θ i for x i Axis and x d Axis angle.

[0119] Before the experiment, the axial error and radial error of each tooth of the milling cutter were detected by a tool measuring instrument to identify the corresponding tool tip point. s ij ; The tool measuring instrument is Zoller genius3 tool measuring instrument, as shown in Table 1. Wherein, Δ zij is the axial error of the cutter teeth, Δ r ij is the radial error of the cutter teeth, spindle speed n The milling cutter feed speed is 1290rpm v f The milling depth is 573mm / min. a p 10mm, milling width a e is 0.5mm, and the milling efficiency is 2865mm 3 / min.

[0120]

[0121] In the experiment, a transient signal test and analysis system was used to obtain the milling vibration displacement signal; the transient signal test and analysis system was DH5922 transient signal test and analysis system. The results are shown in Figure 2 shown.

[0122] After the experiment, the white light interferometer CCI·MP was used to detect the surface morphology of the component processing;

[0123] Finally, the moment when the milling cutter enters the workpiece is calculated. , and the measurement length of the white light interferometer Corresponding milling cutter cutting time ,as follows:

[0124] (1)

[0125] (2)

[0126] in, is the spindle speed; is the workpiece coordinate system, The milling cutter corresponding to the start time of vibration signal acquisition The position of the axis, For machining surface morphology The sampling position of the axis, is the sampling interval, for The corresponding milling cutter cutting time, for The corresponding milling cutter cutting time, is the maximum radial radius of the milling cutter teeth, is the cutting feed speed.

[0127] The step 2 comprises:

[0128] According to Table 1 and Figure 2 , according to the axial error of the cutter teeth From small to large, obtain the characteristic curve of the machined surface morphology changing along the milling cutter feed direction within the distribution range of the cutter tooth axial error, such as Figure 3 As shown, the position of the morphology curve satisfies:

[0129] (3)

[0130] in, is the measurement height of the white light interferometer, The milling cutter corresponding to the start time of vibration signal acquisition The position of the axis, It is the sampling position of the surface topography along the cutting depth direction;

[0131] The root mean square of the surface topography characteristic curve processed at different positions along the milling cutter feed direction , Kurtosis and main frequency , and the RMS of milling vibration in the corresponding period , Kurtosis and main frequency , construct the distribution sequence of machined surface morphology characteristics and milling vibration characteristics in different tooth axial error distribution intervals, and characterize the distribution sequence of machined surface morphology under the influence of milling vibration and tooth error, as follows:

[0132] (4)

[0133] (5)

[0134] in, They are the kurtosis, RMS value and main frequency sequence of the machined surface morphology in different tooth axial error distribution ranges; They are the RMS value, kurtosis and main frequency sequence of milling vibration respectively.

[0135] in accordance with Figure 2 , Figure 3 , using equations (1) to (5), the time-frequency characteristic curves of the machined surface morphology and milling vibration along the milling cutter feed direction are obtained as follows: Figure 4 As shown in the figure, M x w , M y w , M z w They are x , y , z The root mean square sequence of milling vibration displacement in the direction, K xw , K y w , K z w They are x , y , z The milling vibration displacement kurtosis sequence in the direction, F x w , F y w , F z w They are x , y , z The main frequency sequence of milling vibration displacement in the direction.

[0136] Depend on Figure 4 It can be seen that along the feed direction of the milling cutter, the time-frequency characteristic parameters of milling vibration and machined surface morphology show obvious variability. This result shows that during the milling of aviation components, the milling vibration and the process of machined surface morphology formation are in an unstable state and have multi-time-variable characteristics.

[0137] in accordance with Figure 1 , Figure 2 According to equation (3), affected by the axial error of the cutter teeth, the number and distribution of the cutter teeth involved in cutting are different at different axial positions of the milling cutter, which directly changes the formation process of the machined surface morphology, resulting in obvious differences in the change characteristics of the machined surface morphology at different axial positions of the milling cutter. Among them, the difference in the main frequency change characteristics is the largest.

[0138] The milling surface morphology distribution characteristics are used as the reference sequence. o-xyz The distribution characteristics of the milling vibration displacement signals in three directions are used as a comparison sequence, and the grey correlation analysis method is used to obtain the relative correlation degree. The solution results are shown in Table 2. S ( z j ) is the processing surface morphology sequence, w is the milling vibration displacement sequence; M is the root mean square value, K is the kurtosis, F The main frequency.

[0139]

[0140] As shown in Table 2, the correlation between milling vibration and the distribution of machined surface topography is greater than 0.55, showing a strong correlation characteristic. Among them, the correlation between 0.55-0.60 accounts for 4.4%, 0.60-0.70 accounts for 24.4%, 0.70-0.80 accounts for 31.1%, 0.80-0.90 accounts for 26.7%, and greater than 0.90 accounts for 13.4%, indicating that milling vibration has a significant impact on the milling surface topography, and the influence of milling vibration in the three directions is different.

[0141] It is also found that the correlation between kurtosis, RMS value and main frequency changes with the axial position of the milling cutter. Among them, the correlation of main frequency changes most significantly. The above results show that the tooth error and the number of teeth involved in cutting directly change the distribution of machined surface morphology at different positions, which in turn changes the influence of milling vibration on the machined surface morphology at different axial positions of the milling cutter.

[0142] The step 3 comprises:

[0143] The instantaneous cutting posture of the solid carbide end mill under the conditions of cutter tooth error and milling vibration is as follows: Figure 5 As shown in Figure 2, according to the instantaneous cutting posture of the solid carbide end mill under the conditions of cutter tooth error and milling vibration, Figure 5 middle, x a , y a , z a Respectively, they are the length, width, and height of the workpiece; establish The cutting coordinate system, and Coordinate system of milling cutter without vibration, g c ( x , y , z )for o c The trajectory of a point; g d ( x , y , z )for o d The trajectory of a point; g i ( x , y , z )for o i The trajectory of a point; inclination δ c ( t ), δ d ( t )and δ i ( t );

[0144] Depend on Figure 1 and Figure 5 , in the cutter tooth coordinate system, the cutter tooth Cutting edge equation for:

[0145] (6)

[0146] in ， is the blade tooth coordinate system, The tip of the blade The rotation center of Axis through origin And point to point, Axis and parallel, It is the lag angle of any point of the cutting edge relative to the tool tip;

[0147] Depend on Figure 5 , the relationship between the cutting coordinate system and the workpiece coordinate system is:

[0148] (7)

[0149] and Axis relative to Instantaneous inclination of the axis and for:

[0150] (8)

[0151] in, is the milling cutter coordinate system The instantaneous position angle deviation between the axis and the workpiece coordinate system; is the tooth coordinate system The instantaneous position angle offset of the axis and workpiece coordinate system is as follows:

[0152] (9)

[0153] and Axis relative to Instantaneous position angle of the shaft ,as follows:

[0154] (10)

[0155] (11)

[0156] (12)

[0157] From equations (6) to (12), using the trajectory of any point on the cutting edge of the cutter tooth, the equation of the tooth cutting transition surface under the influence of the cutter tooth error and milling vibration is obtained as follows:

[0158] (13)

[0159] in, Cutting teeth i The cut-in and cut-out moments;

[0160] Depend on Figure 1 , Figure 5 , Equation (7) to Equation (12), the relationship between the workpiece coordinate system and the cutter tooth coordinate system is constructed as follows:

[0161] (14)

[0162] in, R 1 is the rotation matrix of the cutting coordinate system and the milling cutter coordinate system without vibration, R 2. R 3 is the rotation matrix between the milling cutter coordinate system and the milling cutter coordinate system without vibration, R 4 is the rotation matrix of the milling cutter coordinate system and the tooth coordinate system; T 1 is the translation matrix between the workpiece coordinate system and the cutting coordinate system, T 2 is the translation matrix between the milling cutter coordinate system and the milling cutter coordinate system without vibration, T 3 is the translation matrix of the milling cutter coordinate system and the tooth coordinate system; the above matrix can be obtained by Figure 4 and (7)~(12); the above matrix can be obtained by Figure 5 Determined by equations (7) to (12).

[0163] for The trajectory of a point;

[0164] (15)

[0165] for The trajectory of a point;

[0166] (16)

[0167] for The trajectory of a point;

[0168] (17)

[0169] The upper and lower boundaries of the trajectory of any point on the cutting edge participating in cutting within time are:

[0170] (18)

[0171] in, is the trajectory equation of tool tip point;

[0172] From formula (13), the intersection line of any adjacent transition surfaces can be obtained as:

[0173] (19)

[0174] Using equations (6) to (19), we can solve the cutting motion trajectory of each reference point of the cutting edge of the cutter and the intersection of other cutting transition surfaces of the cutter teeth to extract y Towards the minimum intersection point, identify the residual cutting transition surface of the cutter teeth, and obtain the distribution of the machined surface morphology, such as Figure 6 shown; e i , e i+1 Cutting teeth i and blade teeth i +1Any point on the cutting edge; Δ x f The trajectory of two adjacent teeth is x The increment in the direction, ignoring vibration and tooth error, Δ x f and f z equal.

[0175] On the workpiece xoy In the coordinate system Arbitrary point establishment and workpiece coordinate system y Axis parallel lines L 1. Straight line L 1. Traverse from the machined surface to the end point of the machined surface to obtain the intersection point with the instantaneous cutting transition surface of the milling cutter teeth;

[0176] straight line L The intersection of 1 and each tooth trajectory is:

[0177] (20)

[0178] Each intersection point is based on y The point set sequence with coordinate values ​​from small to large is:

[0179] (twenty one)

[0180] According to formula (21), when the straight line Traverse from the starting point of the machined surface to the end point of the machined surface and obtain y The sequence of intersection points toward the minimum value is:

[0181] (twenty two)

[0182] According to formula (22), the milling surface morphology is established for:

[0183] (twenty three).

[0184] According to Table 1 and equations (6) to (23), we can obtain Figure 2 The surface morphology distribution solution results of the corresponding position are as follows: Figure 7 As shown. z j t In order to solve the characteristic curve of the machined surface topography, z j s Surface morphology characteristic curve for experimental processing

[0185] Depend on Figure 8 It can be seen that the calculated surface morphology no longer strictly adheres to the periodic consistency along the milling feed direction; there is a significant similarity between the calculated surface morphology and the white light detected milling surface morphology.

[0186] Using equations (1) to (5), the time-frequency characteristic parameters of the milling surface morphology along the feed direction of the milling cutter are identified, and the relative correlation between the surface morphology solution and the experiment is obtained, as shown in Table 3.

[0187] Table 3 Correlation between machined surface topography solution and experiment

[0188]

[0189] It can be seen from Table 3 that the correlation between the distribution characteristics of the machined surface morphology experiment and the solution results is greater than 0.70, showing a strong correlation characteristic. Among them, the correlation degree is 0.70-0.80, accounting for 53.3%, 0.80-0.90, accounting for 26.7%, and greater than 0.90, accounting for 20%, indicating that the solution of the machined surface morphology is relatively accurate.

[0190] The step 4 comprises:

[0191] Using equations (6) to (23), the milling surface morphology under the cutting parameters in Table 1 is solved. The results are as follows: Fig. 9 shown.

[0192] like Fig. 9As shown in (a), the surface morphology affected by down milling and cutting parameters shows high consistency along the feed direction, but lags in the direction of the milling cutter axis, showing diversity.

[0193] like Fig. 9 As shown in (b), affected by the radial error of the cutter teeth, the machined surface morphology does not show the regular distribution within the period under the multi-tooth equal pitch cutting conditions, but becomes the morphology distribution result under the condition of approximately unequal pitch milling.

[0194] like Fig. 9 As shown in (c), affected by the axial error of the cutter teeth, the machined surface morphology presents a multi-tooth unequal pitch milling method along the axial direction of the milling cutter, and the distribution of the machined surface morphology along the feed direction presents a strict regular consistency. The axial error of the milling cutter causes the machined surface morphology to produce a variable distribution along the axial direction.

[0195] like Fig. 9 As shown in (d), affected by the multi-time-variable milling vibration, the machined surface morphology shows an obvious multi-variable distribution, and the morphological characteristic curves of each region are similar. Affected by the multi-time-variable milling vibration, the distribution of the milled surface morphology no longer strictly follows the periodic distribution.

[0196] According to equations (1) to (5), solve Fig. 9 The time-frequency domain characteristic parameters of the milling surface morphology, such as Fig.10 As shown. M j m , K j m , F j m , M j r , K j r , F j r , M j z , K j z , F j z , M j v , K j v , F j vThey are the root mean square value, kurtosis and main frequency sequence of the machined surface morphology under the influence of down milling and cutting parameters, the influence of cutter tooth axial error, the influence of cutter tooth radial error and milling vibration.

[0197] Depend on Fig.10 It can be seen that under the influence of down milling and cutting parameters, the axial error of the cutter teeth and the radial error of the cutter teeth, the machined surface morphology presents a periodic distribution; under the influence of time-varying milling vibration, the machined surface morphology presents diversity.

[0198] In order to verify the influence of tooth error and vibration on the milling surface morphology, the distribution characteristics of the machined surface morphology under the action of tooth error and vibration conditions are correlated with the distribution characteristics of the milling surface morphology. Taking the surface morphology distribution characteristic parameters under the conditions of tooth error and milling vibration as the reference sequence and the surface morphology characteristic parameters under the conditions of tooth error and vibration as the comparison sequence, this method can effectively reveal the influence of tooth error and milling vibration on the formation of machined surface morphology, and its diverse influencing factors are identified as shown in Table 4.

[0199] Table 4 Influence characteristics of milling surface morphology diversity

[0200]

[0201] As shown in Table 4, the correlation between milling vibration, cutter tooth error and machined surface topography distribution is greater than 0.50, showing a strong correlation characteristic. Milling vibration and machined surface topography distribution show a strong correlation characteristic. At the same time, it is found that the correlation between the root mean square value, kurtosis and main frequency changes with the change of the axial position of the milling cutter. The above results confirm that milling vibration has the most obvious influence on the formation of machined surface topography, followed by the influence of the milling cutter tooth structure error on the formation of machined surface topography.

[0202] According to the factors affecting the diversity of surface morphology in efficient milling of aviation components, a method for identifying the time-lapse variability of milling surface morphology is proposed. Fig.11 shown.

[0203] Step 4.1, input milling process plan;

[0204] (4.1)

[0205] Where P is the set of milling process solutions, P1 is the structure and material parameters of the aviation component, P2 is the milling method, P3 is the machine tool parameters, P4 is the milling cutter material parameters, and P5 is the set of milling cutter and cutter tooth structure parameters. D is the diameter of the milling cutter shank, l 1 is the total length of the milling cutter, l 2 is the overhang of the milling cutter, l 3 is the axial length of the cutting edge,β is the cutting edge helix angle, Δ z ij is the axial error of the cutter teeth, Δ r ij is the radial error of the cutter teeth, P6 is the set of milling processing parameters, n is the spindle speed, v f is the milling cutter feed speed, a p is the milling depth, a e is the milling width.

[0206] Step 4.2, sampling method for detecting milling surface morphology;

[0207] (4.2)

[0208] Where P7, P8, and P9 are the sampling methods for milling surface topography detection. z 0 The milling cutter corresponding to the start time of vibration signal acquisition z The position of the axis, x 0 is the milling cutter corresponding to the start time of vibration signal acquisition x The position of the axis, x k For machining surface morphology x The sampling position of the axis, z j is the sampling position of the surface morphology along the cutting depth direction; Δ x k is the sampling interval, Δ x is the measuring length of the white light interferometer, Δ z is the measurement height of the white light interferometer; the moment when the milling cutter cuts into the workpiece t 0, t k for x k Corresponding to the milling cutter cutting moment, the measured length Δ of the white light interferometer x Corresponding milling cutter cutting time Δ t x , Δ t k is Δ x k Corresponding milling cutter cutting time; M j S , K j S , F j S They are the kurtosis, RMS value and main frequency sequence of the machined surface morphology in different tooth axial error distribution ranges; M w , K w , F w They are the RMS value, kurtosis and main frequency sequence of milling vibration respectively.

[0209] Step 4.3, milling cutter trajectory and instantaneous milling cutter posture;

[0210] (4.3)

[0211] In the formula, For milling cutter o d The trajectory of the point, δ d ( t )for z d Axis relative to z The instantaneous inclination of the axis, φ d ( t )for x d Relative to x The instantaneous position angle of the shaft; For milling cutter o i The trajectory of the point, δ i ( t )for z i Axis relative to z The instantaneous inclination of the axis, φ i ( t )for x i Relative to x The instantaneous position angle of the shaft.

[0212] Step 4.4, cutter tooth cutting edge equation, cutter tooth cutting transition surface and cutting boundary;

[0213] (4.4)

[0214] In the formula, E i ( x i , y i , z i ) is the blade tooth s ij The cutting edge equation is Gi ( x , y , z ) is the equation of the tooth cutting transition surface under the influence of tooth error and milling vibration, h ij for[ t 2, t 4] The upper and lower boundaries of the trajectory of any point on the cutting edge involved in cutting within the time period,

[0215] Step 4.5, the intersection line of any adjacent transition surfaces;

[0216] (4.5)

[0217] In the formula, f i ( x , y , z ) is the intersection line of any adjacent transition surfaces.

[0218] Step 4.6, the milling cutter teeth instantaneously cut the intersection of the transition surface;

[0219] (4.6)

[0220] In the formula, q c For straight line L 1 is the intersection point with each tooth trajectory line.

[0221] Step 4.7, the minimum node set sequence of the milling surface morphology in the y direction;

[0222] (4.7)

[0223] In the formula, for y Towards the minimum intersection point sequence.

[0224] Step 4.8, milling surface morphology collection;

[0225] (4.8)

[0226] In the formula, C is the set of surface morphologies to be solved, q ij is the set of shape intersection points, G ij It is the residual transition surface.

[0227] Step 4.9, solving the milling parameters affecting the machined surface morphology set;

[0228] (4.9)

[0229] Where C0 is the set of milling parameters affecting the machined surface morphology.

[0230] Step 4.10, a set of machined surface morphologies under the action of tool radial error, a set of machined surface morphologies under the action of tool tooth axial error, and a set of machined surface morphologies under vibration conditions;

[0231] (4.10)

[0232] Where C1 is the set of surface morphologies machined under the action of radial tooth error, C2 is the set of surface morphologies machined under the action of axial tooth error, and C3 is the set of surface morphologies machined under vibration conditions.

[0233] Step 4.11, evaluate the correlation between various tool tooth errors and vibration conditions and the machined surface topography;

[0234] (4.11)

[0235] In the formula, is the relative correlation between C0, C1, C2, C3 and C

[0236] Step 4.12, whether it is greater than or equal to the correlation threshold, according to the preset threshold, determine which errors and disturbance conditions have a significant impact on the machined surface morphology;

[0237] (4.12)

[0238] In the formula, To calculate the relative correlation, is the relative correlation threshold.

[0239] Step 4.13, time-lapse variability identification method for surface morphology of efficient milling of aviation components.

[0240] Fig.11 In the figure, P is a set of milling process solutions, P1 is the structure and material parameters of aviation components, P2 is the milling method, P3 is the machine tool parameters, P4 is the milling cutter material parameters, P5 is the milling cutter and cutter tooth structure parameter set, P6 is the milling processing parameter set; P7, P8, P9 are the milling surface morphology detection sampling method sets.

[0241] A is the vibration signal distribution sequence, B is the machined surface morphology distribution sequence, C is the set of solved machined surface morphologies, C0 is the set of solved machined surface morphologies affected by milling parameters, C0 is the set of solved machined surface morphologies affected by milling parameters, C1 is the set of solved machined surface morphologies under the action of radial error of cutter teeth, C2 is the set of solved machined surface morphologies under the action of axial error of cutter teeth, and C3 is the set of solved surface morphologies under vibration conditions;q ij is the set of shape intersection points, G ij is the residual transition surface; is the relative correlation between C0, C1, C2, C3 and C, is the relative correlation threshold.

[0242] This method reveals the formation of milling surface morphology based on the dynamic characteristics of instantaneous cutting behavior under conditions of tooth error and milling vibration; according to the surface morphology solution method, the surface morphology under different influencing factors is solved to characterize the diversity of milling surface morphology distribution; the time-frequency characteristic analysis method and grey correlation analysis are used to identify the influencing characteristics of the time-shift variability of the surface morphology distribution.

[0243] The step 5 comprises:

[0244] The time-lapse multi-variable response analysis and experimental verification method of the milling titanium alloy surface morphology are as follows:

[0245] Step 1: Input different cutting process plans;

[0246] Step 2, solving the instantaneous cutting posture of milling vibration;

[0247] Step 3: Process the surface solution model to identify the influencing characteristics of different cutting process solutions;

[0248] Step 4: Compare the correlation of distribution characteristics of different cutting process solutions;

[0249] Step 5, solving the comparison of distribution characteristics of the processed surface morphology;

[0250] Step six: Comparison of surface morphology distribution characteristics of experimental processing.

[0251] The specific calculation process is as follows:

[0252] According to the instantaneous cutting behavior of the milling cutter, the second set of process schemes is designed. The experimental scheme in Section 2 is used as Scheme 1. The equipment used in the experiment and the experimental site layout are the same as Section 2. Feed speed v f , cutting depth a p , cutting width a e The spindle speed remains unchanged. n The specific milling parameters are shown in Table 5.

[0253]

[0254] Extract the vibration displacement signal of the experiment and the surface morphology of the machined surface after the experiment is completed, such as Fig.12 shown.

[0255] Depend on Fig.12 It can be seen that the vibration displacement signal of Scheme 2 is significantly different from that of Scheme 1. x The vibration amplitude in the direction is greater than that in other directions, and the distribution characteristics of the vibration signal, such as the root mean square value, kurtosis and main frequency distribution, show obvious variability.

[0256] The experimental results of Scheme 2 show that although the milling surface morphology is affected by multiple factors and has a complex shape, it still significantly presents layered characteristics and unequal tooth pitch cutting effects; the distribution characteristics of the machined surface morphology are relatively stable, which has changed compared to Scheme 1.

[0257] In order to determine the correctness of the cutting behavior response characteristics of the tooth distribution milling cutter obtained by changing the process parameters, the Fig.11 The time-lapse variability identification method of milling surface morphology is solved. The distribution of milling surface morphology is as follows: Fig.13 shown.

[0258] Depend on Fig.13 It can be seen that the comparison of the solution results of the two schemes shows that increasing the rotation speed not only reduces the residual height and distribution spacing of the morphology, but also reduces the vibration amplitude by reducing the feed per tooth and the volume of the cutting layer. Therefore, according to the solution, the second set of schemes provides a better morphology distribution effect. The correlation between the surface morphology of the machined surface solved by Scheme 2 and the experiment is shown in Table 6.

[0259]

[0260] It can be seen from Table 6 that the correlation between the surface topography calculated by Scheme 2 and the distribution characteristics of the experimental results is highly correlated, which proves the correctness of the surface topography solution method for milling.

[0261] use Fig.11 The time-lapse variability recognition method of milling surface morphology is used to solve the problem. The results are as follows Fig.14 shown.

[0262] like Fig.14 As shown in (a), the influence of cutting parameters, the machined surface morphology also shows a high consistency, but the maximum height of the morphology residue is also reduced after the cutting parameters are changed, indicating that the change of rotation speed will affect the distribution spacing and height of the morphology residue.

[0263] like Fig.14 As shown in (b), affected by the distribution of the radial error of the cutter teeth, although the maximum radial error of the cutter teeth in Scheme 2 is greater than that in Scheme 1, the maximum residual height of the morphology is less than that in Scheme 1, indicating that the change in rotation speed has a greater impact on the surface morphology than the radial error of the cutter teeth.

[0264] like Fig.14 As shown in (c), the surface morphology of Scheme 2 is affected by the axial error of the cutter teeth and also has diversity. It is divided into five layers along the axis of the milling cutter. However, due to the changes in the sequence of cutter teeth involved in milling and the change in the axial error, there are differences in the distribution of morphology within the cycle.

[0265] like Fig.14 As shown in (d), affected by the milling vibration, the distribution of the machined surface morphology presents an extremely complex distribution characteristic, and when the tooth error is not considered, the morphology is affected by the change of vibration characteristics, and the diversity of the surface morphology is different from that of Scheme 1.

[0266] According to the milling processing parameters of Scheme 2, the time-frequency domain characteristic parameters of the milling surface morphology are solved. The time-frequency distribution characteristics of the machined surface morphology under the influence of various factors in Scheme 2 are as follows: Fig.15 shown.

[0267] Depend on Fig.15 It can be seen that Scheme 2 shows similar distribution characteristics to Scheme 1 under the influence of down-milling and cutting parameters, axial error of the cutter teeth and radial error of the cutter teeth; the morphology at any position under the influence of milling vibration is inconsistent, resulting in the diversity of the machined surface morphology.

[0268] In order to verify the correctness of the above analysis results and determine the correctness of the diversity of milling surface morphology distribution during milling under different process schemes, the surface morphology distribution characteristics at different positions of Scheme 2 and the surface morphology distribution characteristics of the solved machined surface are analyzed for relative correlation, such as Fig.16 As shown. ϒ 1. ϒ 2. ϒ 3. ϒ 1 ′ , ϒ 2 ′ , ϒ 3 ′ They are the influence of radial error of cutter teeth, the influence of axial error of cutter teeth, the influence of milling vibration and the correlation of solving the surface morphology of machining for scheme 1 and scheme 2 respectively.

[0269] Depend on Fig.16 It can be seen that the identification of the factors affecting the variability of Scheme 2 is similar to that of Scheme 1, indicating that under the two different processing schemes, the milling parameters and tools are different, but the impact on the final machined surface morphology is highly consistent. The correlation degree of the single factor on the milling surface morphology is greater than 0.5. The vibration has the greatest impact on the formation of the surface morphology of the end mill milling cutter, revealing that the milling vibration of the workpiece system is the main factor that causes the deterioration of the surface quality. The structure of the milling cutter has the second greatest impact on the formation of the milling surface morphology, indicating that the geometric accuracy of the tool itself is still important for the formation of the surface morphology.

[0270] Comparison and analysis of the correlation between the vibration displacement obtained from the two milling experimental schemes and the time-frequency characteristic change curves of the machined surface morphology, such as Fig.17 shown.

[0271] Depend on Fig.17 It can be seen that the correlation between milling vibration and machined surface topography distribution is greater than 0.55, showing a strong correlation characteristic. The above results confirm that the change of cutting parameters leads to the change of milling vibration displacement, and then the formation of milling surface topography changes, and the distribution of machined surface topography shows a time-varying characteristic. This result shows that milling vibration is the dominant factor in the formation of machined surface topography.

[0272] In order to verify the effectiveness of the time-frequency characteristics of the milling surface morphology, the root mean square value, kurtosis and main frequency of the morphology under the two milling schemes are solved. The solution results are shown in Fig.18 As shown, the experiment Fig.19 shown.

[0273] Depend on Fig.18 ,19,The time-frequency characteristic change curves of the surface morphology of the two experimental schemes show certain similarities, but also have variability, indicating that under two different processing schemes, the tool tooth error affects the formation mechanism of the milling surface morphology.

[0274] In summary, the model and method constructed in this paper can realize the correct solution of the distribution characteristics of the milling surface morphology and the identification of the response characteristics under different process conditions, and reveal the influence of factors such as cutting parameters, tooth error, and milling vibration on the formation of the milling surface.

[0275] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be arranged and combined, and those skilled in the art can exhaust all possibilities based on the mathematical knowledge of arrangement and combination. Therefore, the present invention will no longer describe the technical solutions after arrangement and combination one by one, but it should be understood that the technical solutions after arrangement and combination have been disclosed by the present invention.

[0276] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for identifying and verifying the time-lapse variability of surface topography processed by an end mill under vibration conditions, characterized in that: include: Step 1: Design an experimental plan for milling vibration and surface morphology of titanium alloy by end mill: An experiment on efficient milling of titanium alloy was conducted using an integral end mill, and the milling vibration signal was extracted from the machining process. Using the milling vibrations at different positions at different times, a method for analyzing the time-frequency characteristic parameters of milling vibration and machined surface morphology was proposed to characterize the variability of milling surface morphology distribution. Step 2: Design a method for constructing a sequence of surface topography distribution of end mill machining under vibration conditions: By using the milling surface topography, the characteristic parameter sequence of the milling surface topography is constructed to reveal the influence of the cutter tooth error and vibration on the machined surface topography. Step 3: Establish a time-lapse multi-variability solution model for the machining surface morphology under the influence of vibration: Using the instantaneous cutting posture of the milling cutter, a method for calculating the machined surface topography is constructed to reveal the formation mechanism of the machined surface topography. Step 4: Design an efficient milling surface topography distribution characteristics identification method: The time-frequency analysis method of the machined surface morphology characteristic curve is used to characterize the distribution characteristics of the machined surface morphology; Step 5: Design the time-lapse multi-variable response analysis and experimental verification method of the processed surface morphology: A method for calculating the time-lapse variability of milling surface topography is proposed to reveal the influence of cutting parameters, cutter tooth errors and milling vibration on the surface topography; the response characteristics of the time-lapse variability of the surface topography of high-efficiency milling of aviation components are studied and verified; The step 1 comprises: Before the experiment, the axial error and radial error of each tooth of the milling cutter were detected by a tool measuring instrument to identify the corresponding tool tip point. ; In the experiment, the transient signal test and analysis system was used to obtain the milling vibration displacement signal; After the experiment is completed, a white light interferometer is used to detect the surface morphology of the component processing; Finally, the moment when the milling cutter enters the workpiece is calculated. , and the measurement length of the white light interferometer Corresponding milling cutter cutting time ,as follows: （1） （2） in, is the spindle speed; is the workpiece coordinate system, The milling cutter corresponding to the start time of vibration signal acquisition The position of the axis, For machining surface morphology The sampling position of the axis, is the sampling interval, for The corresponding milling cutter cutting time, for The corresponding milling cutter cutting time, is the maximum radial radius of the milling cutter teeth, is the cutting feed speed.

2. The method for identifying and verifying the time-lapse variability of the surface topography processed by an end mill under vibration conditions according to claim 1, characterized in that: The step 2 comprises: According to the axial error of the cutter teeth From small to large, obtain the characteristic curve of the machined surface morphology along the milling cutter feed direction within the tooth axial error distribution range, where the position of the morphology curve satisfies: （3） in, is the measurement height of the white light interferometer, The milling cutter corresponding to the start time of vibration signal acquisition The position of the axis, It is the sampling position of the surface topography along the cutting depth direction; The root mean square of the surface topography characteristic curve processed at different positions along the milling cutter feed direction , Kurtosis and main frequency , and the RMS of milling vibration in the corresponding period , Kurtosis and main frequency , construct the distribution sequence of machined surface morphology characteristics and milling vibration characteristics in different tooth axial error distribution intervals, and characterize the distribution sequence of machined surface morphology under the influence of milling vibration and tooth error, as follows: （4） （5） in, They are the kurtosis, RMS value and main frequency sequence of the machined surface morphology in different tooth axial error distribution ranges; They are the RMS value, kurtosis and main frequency sequence of milling vibration respectively.

3. The method for identifying and verifying the time-lapse variability of the surface topography processed by an end mill under vibration conditions according to claim 2, characterized in that: The step 3 comprises: According to the tooth error and milling vibration conditions, the instantaneous cutting posture of the solid carbide end mill is established. The cutting coordinate system, and Coordinate system of milling cutter without vibration; In the cutter tooth coordinate system, the cutter tooth Cutting edge equation for: （6） in, is the blade tooth coordinate system, The tip of the blade The rotation center of Axis through origin And point to point, Axis and parallel, It is the lag angle of any point of the cutting edge relative to the tool tip; The relationship between the cutting coordinate system and the workpiece coordinate system is: （7） and Axis relative to Instantaneous inclination of the axis and for: （8） in, is the milling cutter coordinate system The instantaneous position angle deviation between the axis and the workpiece coordinate system; is the tooth coordinate system The instantaneous position angle offset of the axis and workpiece coordinate system is as follows: （9） and Axis relative to Instantaneous position angle of the shaft ,as follows: （10） （11） （12） From equations (6) to (12), using the trajectory of any point on the cutting edge of the cutter tooth, the equation of the tooth cutting transition surface under the influence of the cutter tooth error and milling vibration is obtained as follows: （13） in, Cutting teeth i The cut-in and cut-out moments; The relationship between the workpiece coordinate system and the cutter tooth coordinate system is: （14） in, is the rotation matrix of the cutting coordinate system and the milling cutter coordinate system without vibration, is the rotation matrix between the milling cutter coordinate system and the milling cutter coordinate system without vibration, is the rotation matrix of the milling cutter coordinate system and the tooth coordinate system; is the translation matrix between the workpiece coordinate system and the cutting coordinate system, is the translation matrix between the milling cutter coordinate system and the milling cutter coordinate system without vibration, is the translation matrix of the milling cutter coordinate system and the tooth coordinate system; the above matrix can be determined by Figure 4 and equations (7) to (12); for The trajectory of a point; （15） for The trajectory of a point; （16） for The trajectory of a point; （17） The upper and lower boundaries of the trajectory of any point on the cutting edge participating in cutting within time are: （18） in, is the trajectory equation of tool tip point; From formula (13), the intersection line of any adjacent transition surfaces can be obtained as: （19） Using equations (6) to (19), we can solve the cutting motion trajectory of each reference point of the cutting edge of the cutter and the intersection of other cutting transition surfaces of the cutter teeth to extract y Towards the minimum intersection point, identify the residual cutting transition surface of the cutter teeth and obtain the distribution of the machined surface morphology; On the workpiece xoy In the coordinate system Arbitrary point establishment and workpiece coordinate system y Axis parallel lines ,straight line Traverse from the machined surface to the end point of the machined surface to obtain the intersection point with the instantaneous cutting transition surface of the milling cutter teeth; straight line The intersection points with each tooth trajectory are: (20) Each intersection point is based on y The point set sequence with coordinate values ​​from small to large is: (21) According to formula (21), when the straight line Traverse from the starting point of the machined surface to the end point of the machined surface and obtain y The sequence of intersection points toward the minimum value is: (22) According to formula (22), the milling surface morphology is established for: (23)。 4. The method for identifying and verifying the time-lapse variability of the surface topography processed by an end mill under vibration conditions according to claim 3, characterized in that: The step 5 comprises: Step 1: Input different cutting process plans; Step 2, solving the instantaneous cutting posture of milling vibration; Step 3: Process the surface solution model to identify the influencing characteristics of different cutting process solutions; Step 4: Compare the correlation of distribution characteristics of different cutting process solutions; Step 5, solving the comparison of distribution characteristics of the processed surface morphology; Step six: Comparison of surface morphology distribution characteristics of experimental processing.

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