Identification method for the changing characteristics of instantaneous friction and wear energy density on the flank of high-efficiency milling cutters

Abstract

A method for identifying the changing characteristics of the energy density of instantaneous friction wear on the flank face of a high-efficiency milling cutter belongs to the field of mechanical processing technology. It includes a method for calculating the instantaneous position of the milling cutter tooth flank face; a model for calculating the instantaneous position of the cutter tooth element and its instantaneous friction velocity; a method for calculating the instantaneous wear depth of the cutter tooth element flank face; a method for calculating the instantaneous wear volume of the cutter tooth element flank face; a method for calculating the instantaneous friction energy consumption of the cutter tooth element flank face; and a method for calculating the instantaneous friction wear energy density of the cutter tooth element flank face. The purpose of this method is to propose a method for calculating the instantaneous wear depth of the cutter tooth flank face, solving the problem that existing methods cannot reveal the changing characteristics of the instantaneous friction wear on the cutter tooth flank face. By using the instantaneous friction wear energy density of the cutter tooth flank face, the dynamic relationship between the instantaneous friction energy consumption and the instantaneous wear volume of the cutter tooth element flank face is revealed, providing a basic model and method for quantitatively describing the formation and evolution of the wear on the flank face of high-feed milling cutters.

Description

Technical Field

[0001] The invention relates to a method for identifying instantaneous friction and wear energy density variation characteristics of a flank face of a high-efficiency milling cutter, and belongs to the technical field of mechanical processing. Background Art

[0002] The transient friction and wear energy density of the milling cutter flank is one of the key components of understanding the dynamic relationship between transient friction and wear on the milling cutter flank. It is also an important indicator for evaluating the friction and wear state of the cutter tooth flank. Establishing a method to calculate the transient friction and wear energy density of the milling cutter flank and analyzing its dynamic distribution characteristics provides guidance for understanding the formation and evolution of flank wear in high-feed milling cutters.

[0003] Existing methods for identifying friction wear on the flank of milling cutters only focus on the overall level of friction energy consumption on the flank and the maximum width and depth of cumulative wear, ignoring the unevenness and variability of friction energy consumption and wear distribution on the flank under the action of milling vibration and tooth wear. The dynamic relationship between instantaneous friction energy consumption and wear volume at different positions on the flank remains to be revealed.

[0004] To this end, the present invention utilizes the transient contact relationship of the tooth flank during the dynamic cutting process of the milling cutter under vibration, proposes a method for solving the instantaneous position and friction speed of the tooth flank of the milling cutter, and uses the analysis results of the instantaneous thermal-mechanical coupling field of the tooth flank to solve the instantaneous wear depth, wear volume and friction energy consumption of the flank during the milling cutter cutting process. A solution model for the instantaneous friction and wear energy density of the tooth flank is constructed, revealing the dynamic relationship change characteristics between the instantaneous friction and wear of the tooth flank. Summary of the Invention

[0005] The purpose of this invention is to utilize the transient position of the tooth element and the instantaneous friction velocity calculation model of the flank face to solve the problem that existing methods ignore the impact of milling vibration and tooth wear on the instantaneous friction and wear state of the flank face. The following is a brief overview of the invention to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive overview of the invention. It is not intended to identify key or important aspects of the invention, nor is it intended to limit the scope of the invention.

[0006] The technical solution of the present invention:

[0007] The identification method of the energy density variation characteristics of the instantaneous friction and wear of the flank face of a high-efficiency milling cutter includes:

[0008] Step 1, the instantaneous pose calculation method of the flank of the milling cutter teeth;

[0009] Step 2: Calculate the instantaneous position and friction velocity of the blade tooth.

[0010] Step 3, the calculation method of the instantaneous wear depth of the tool tooth microelement flank;

[0011] Step 4, the instantaneous wear volume calculation method of the tool tooth microelement flank surface;

[0012] Step 5, the calculation method of the instantaneous friction energy consumption of the blade tooth microelement flank surface;

[0013] Step 6: Calculation method of instantaneous friction and wear energy density of the tool tooth microelement flank.

[0014] Preferably, step 1 includes: determining a milling processing mode, determining the milling cutter and its tooth structure parameters and cutting parameters, and performing milling cutter trajectory and instantaneous posture calculation and tooth microelement instantaneous posture calculation under the action of a milling vibration signal, that is, obtaining the high-feed milling cutter structure and the instantaneous cutting posture of the milling cutter and tooth under the action of vibration;

[0015] The instantaneous posture of the flank face and cutting edge of the cutter tooth is:

[0016]

[0017] In the formula, o-xyz is the workpiece coordinate system, point o is the intersection of the bottom, back and right vertical surfaces of the workpiece, the x-axis is in the same direction as the milling cutter feed direction, the y-axis is in the same direction as the workpiece cutting width direction, and the z-axis is in the same direction as the workpiece cutting depth direction. i -x i y i z i The tooth coordinate system is Figure 2 As shown, the cutting edge abe o The projection to the bottom surface is b1-e o ′-a1, passing e o ′ is a tangent to the bottom surface, and the intersection of the tangent and perpendicular lines through b1 is the origin o i , o i e o ' direction is y i Axis oi b1 is z i Axis, perpendicular to the bottom axis is x i Axis, G i is the back face equation, G i 0 is the cutting edge equation, M is the transformation matrix from the tooth coordinate system to the workpiece coordinate system, M1 is the translation matrix from the tooth coordinate system to the milling cutter structure coordinate system, M2 is the translation matrix from the cutting coordinate system under vibration to the non-vibration cutting coordinate system, M3 is the translation matrix from the non-vibration cutting coordinate system to the workpiece coordinate system, T1 and T2 are the rotation matrices from the tooth coordinate system to the milling cutter structure coordinate system, T3 is the rotation matrix from the milling cutter structure coordinate system to the cutting coordinate system under vibration, and T4 and T5 are the rotation matrices from the vibration cutting coordinate system to the non-vibration cutting coordinate system.

[0018] Preferably, step 2 includes:

[0019] Obtain the instantaneous position and friction velocity of the tooth element and its flank surface;

[0020] The instantaneous contact friction characteristic point e1 between the tooth microelement flank face and the machined transition surface is calculated as:

[0021]

[0022] The common tangent plane equation Q1(x(t), y(t), z(t)=0) is obtained from formula (2), and the instantaneous attitude angle of the tool tooth element in the workpiece coordinate system is obtained as follows:

[0023]

[0024]

[0025] The parametric equation of the tooth flank surface in the workpiece coordinate system is:

[0026]

[0027] Where x Gi (t), y Gi (t), z Gi (t) are the parametric equations of the flank surface of the cutter along the x, y, and z directions respectively;

[0028] According to equations (2) and (5), the motion speed of point e1 on the flank surface of the cutter along the three directions of the workpiece coordinate system is:

[0029]

[0030] Using equations (2) and (6), we can obtain the instantaneous angle β(t) between the normal vector of the common tangent plane at point e1 and the motion velocity v(t). Then, the instantaneous friction velocity v'(t) at point e1 on the flank surface of the tooth element is:

[0031]

[0032] Preferably, step 3 includes:

[0033] Obtain the micro-element flank surface and its instantaneous wear depth under the condition of tooth wear, e1' is the position point of the flank surface after point e1 is worn; v hi (t) is the instantaneous wear depth rate measured along the normal vector of the tangent plane at point e1; η1 is the difference between the normal vector of the tangent plane at point e1 and z i Axis space angle; η2 is the normal vector of the tangent plane at point e1 at x i o i y i Projection on the coordinate plane and xi Axis plane angle; Δx i , Δz i are the coordinate increments of point e1' relative to e1;

[0034] The instantaneous growth rate and instantaneous increment of the wear depth of the tooth element flank face measured along the normal vector direction of the common tangent plane at point e1 are:

[0035]

[0036] Where h i (t) is the cumulative wear depth of the flank surface in the thermal-mechanical coupling field of the cutter tooth as a function of time;

[0037] The instantaneous increase in wear depth causes the tooth edge of the tool to i and z i The instantaneous increment Δx of the direction i (t), Δz i (t) are:

[0038]

[0039] Where η1 and η2 are the normal vector of the tangent plane at point e1 and z respectively. i 、y i The instantaneous angle of the axis;

[0040] According to equations (5), (8), and (9), the equation for calculating the tooth flank surface under wear conditions is:

[0041]

[0042] According to equations (9) to (11), the curve formed by the point where the instantaneous wear depth on the flank surface is 0 is the lower boundary of the instantaneous friction wear on the flank surface of the cutter tooth. At the same time, using equations (1), (8) and (9), the tooth micro-element cutting edge equation under wear conditions and the upper boundary of the instantaneous friction wear on the flank surface of the cutter tooth are obtained.

[0043] Preferably, step 4 includes:

[0044] According to equations (2) and (8) to (10), using the common tangent surface equation at point e1 and the tooth infinitesimal flank surface equation under wear conditions, the instantaneous friction area s of the tooth infinitesimal flank surface is solved within the upper and lower boundaries of the instantaneous friction wear of the tooth flank surface. i , then the instantaneous wear volume growth rate V at point e1 on the tooth edge is i (t) and cumulative wear volume ΣV i for:

[0045]

[0046] Where L is the boundary of the instantaneous friction area at point e1 on the flank surface of the tooth.

[0047] Preferably, step 5 includes:

[0048] In order to accurately identify the changing characteristics of the friction energy consumption in the instantaneous contact area between the flank surface of the cutter tooth and the machined transition surface, a transient friction stress model of the flank surface of the cutter tooth is constructed.

[0049] Using the equivalent stress of the instantaneous thermal-mechanical coupling field on the flank surface of the cutter tooth in the workpiece coordinate system, the stress component along the instantaneous friction velocity direction of the flank surface of the cutter tooth microelement is obtained as follows:

[0050] τ i '(t)=σ x (t)cosγ x +σ y (t)cosγ y +σ z (t)cosγ z (12)

[0051] Where, γ x (t), γ y (t), γ z (t), respectively σ x (t), σ y (t), σ z (t) The angle between it and the friction speed;

[0052] According to equations (7) and (12), the instantaneous friction energy consumption P at any point on the blade edge is i (t), and the cumulative friction energy consumption ΣE i for:

[0053]

[0054] Where, t j , t j+1 They are the start time and end time of cutting of the cutter teeth respectively.

[0055] Preferably, step 6 includes:

[0056] According to equations (12) and (13), the instantaneous friction and wear energy density e at any point on the tooth flank is i (t), and the average friction and wear energy density during the tooth cutting period for:

[0057]

[0058] Where, the instantaneous friction wear energy density e of the tooth microelement flank surface is i(t), represents the instantaneous anti-friction and wear capability of the flank surface; average friction and wear energy density It indicates the level of resistance to friction and wear of the flank surface of the tooth during the cutting process.

[0059] The present invention has the following beneficial effects:

[0060] 1. This paper proposes a method for calculating the instantaneous wear depth of the tooth flank, resolving the problem that existing methods cannot reveal the changing characteristics of the instantaneous friction wear of the flank. By using the instantaneous friction wear energy density of the tooth flank, the dynamic relationship between the instantaneous friction energy consumption and the instantaneous wear volume of the flank is revealed, providing a basic model and method for quantitatively describing the formation and evolution of flank wear on high-feed milling cutters.

[0061] 2. Existing research on milling cutter tooth wear has primarily focused on the maximum wear width of the tooth flank, ignoring the dynamic changes in the tooth wear state during the cutting process. This has failed to reveal the evolutionary characteristics of the wear depth and wear volume of the tooth flank. This invention, by constructing a method for calculating the instantaneous wear depth and wear volume of the tooth flank microelement, quantitatively reveals the changing characteristics of the friction wear state of the tooth flank.

[0062] 3. Most existing methods for calculating the friction energy consumption of the flank face of milling cutter teeth rely on auxiliary equipment such as experimental testing, ignoring the formation and evolution of the friction energy consumption of the flank face during the entire milling process. This method uses finite element simulation to extract the tribological characteristic variables of the corresponding feature points and construct a method for calculating the instantaneous friction energy consumption of the flank face of the cutter tooth microelement.

[0063] 4. Most of the existing research on the wear reduction and anti-wear of the milling cutter flank has tested the wear life of the corresponding teeth through experiments. The present invention further constructs a solution method for the instantaneous friction wear energy density of the tooth micro-element flank surface by solving the instantaneous wear depth, instantaneous wear volume, and instantaneous friction energy consumption of the tooth micro-element flank surface, and conducts a difference study, which can provide a basis for predicting the wear reduction and anti-wear ability of the tooth flank surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a flow chart of the method for identifying the changing characteristics of the instantaneous friction and wear energy density of the flank face of a high-efficiency milling cutter of the present invention;

[0065] Figure 2 Schematic diagram of the milling cutter structure and its instantaneous cutting posture of the present invention;

[0066] Figure 3 Schematic diagram of the blade tooth micro-element structure and its instantaneous posture of the present invention;

[0067] Figure 4 This is a distribution diagram of vibration acceleration signals in a milling experiment of the present invention;

[0068] Figure 5 1 is a graph showing the instantaneous friction velocity change of the blade flank of the present invention, wherein (a) is blade 1, (b) is blade 2, and (c) is blade 3;

[0069] Figure 6 Schematic diagram of the tooth microelement flank surface under wear conditions of the present invention;

[0070] Figure 7 This is the instantaneous wear boundary distribution diagram of the cutter teeth of the present invention, where (a) is cutter tooth 1, (b) is cutter tooth 2, and (c) is cutter tooth 3;

[0071] Figure 8 1 is a dynamic curve diagram of the instantaneous wear depth change rate of the blade flank of the present invention, wherein (a) is blade 1, (b) is blade 2, and (c) is blade 3;

[0072] Figure 9 1 is a dynamic curve diagram of the instantaneous wear volume change rate of the blade flank of the present invention, wherein (a) is blade 1, (b) is blade 2, and (c) is blade 3;

[0073] Figure 10 This is the instantaneous friction velocity and friction force distribution diagram of the blade flank of the present invention;

[0074] Figure 11 1 is a dynamic change curve of the instantaneous friction energy consumption per unit area of ​​the blade flank of the present invention, wherein (a) is blade tooth 1, (b) is blade tooth 2, and (c) is blade tooth 3;

[0075] Figure 12 1 is a graph showing the dynamic change of the instantaneous friction and wear energy density of the flank surface of the cutter teeth of the present invention, wherein (a) is cutter tooth 1, (b) is cutter tooth 2, and (c) is cutter tooth 3;

[0076] Figure 13 Schematic diagram of characteristic variables of friction and wear of the flank surface of the cutter teeth of the present invention, wherein (a) is the average friction and wear energy density of a milling cutter cutting cycle, (b) is the minimum friction and wear energy density of a milling cutter cutting cycle, (c) is the maximum friction and wear energy density of a milling cutter cutting cycle, and (d) is the cumulative friction energy consumption of a milling cutter cutting cycle;

[0077] Figure 14 2 is a comparative analysis of the differences in friction and wear characteristic parameters at different positions on the flank of the cutter teeth of the present invention, wherein (a) is cutter tooth 1, (b) is cutter tooth 2, and (c) is cutter tooth 3;

[0078] Figure 15 This is a distribution diagram of the experimental results of the cumulative wear depth of the flank surface of the cutter teeth of the present invention;

[0079] Figure 16 3. This is a comparison analysis diagram of the significance of the characteristic parameters of the flank wear of the cutter teeth of the present invention, wherein (a) is cutter tooth 1, (b) is cutter tooth 2, and (c) is cutter tooth 3. DETAILED DESCRIPTION

[0080] To make the objectives, technical solutions, and advantages of the present invention more clearly apparent, the present invention is described below using specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely illustrative and are not intended to limit the scope of the present invention. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present invention.

[0081] The connections mentioned in the present invention are divided into fixed connections and detachable connections. The fixed connections (i.e., non-detachable connections) include but are not limited to conventional fixed connection methods such as hemming, rivet connection, bonding connection, and welding connection. The detachable connections include but are not limited to conventional detachable methods such as threaded connection, snap connection, pin connection, and hinge connection. When the specific connection method is not clearly specified, it is assumed that at least one connection method can always be found among the existing connection methods to achieve the function. Those skilled in the art can choose according to their needs. For example: a welded connection is selected for a fixed connection, and a hinge connection is selected for a detachable connection.

[0082] Specific implementation method 1: Combination Figures 1-16 This embodiment describes a method for identifying the energy density variation characteristics of the instantaneous friction wear of the flank face of a high-efficiency milling cutter. This method utilizes the instantaneous cutting posture of the milling cutter and the cutter teeth under vibration, adopts the microelement method to construct a solution model for the instantaneous wear depth and wear volume of the cutter tooth flank face, proposes a solution method for the instantaneous friction characteristic variables of the cutter tooth flank face, and proposes a method for identifying the energy density variation characteristics of the instantaneous friction wear of the milling cutter flank face based on the solution results of the friction characteristic variables of the cutter tooth flank face.

[0083] By identifying and characterizing the characteristic variables of instantaneous friction on the flank surface of the cutter tooth, and using the results of the dynamic difference analysis of the friction and wear energy density at different positions on the flank surface of the cutter tooth, the dynamic distribution characteristics of the instantaneous friction and wear on the flank surface of the cutter tooth are quantitatively described, including:

[0084] Step 1, the instantaneous pose calculation method of the flank of the milling cutter teeth;

[0085] Determine the milling processing mode, determine the milling cutter and its tooth structure parameters and cutting parameters, and under the action of the milling vibration signal, perform milling cutter trajectory and its instantaneous posture solution and tooth microelement instantaneous posture solution, that is, obtain the high feed milling cutter structure and the instantaneous cutting posture of the milling cutter and tooth under the action of vibration;

[0086] In order to construct the instantaneous pose solution method of the cutter tooth microelement, the instantaneous pose of the flank of the milling cutter tooth under vibration is first solved, as shown in the following example: Figure 2 As shown, Figure 2 The explanation of each milling cutter structure and its instantaneous cutting posture variables are shown in Table 1.

[0087] Table 1 Milling cutter structure and its instantaneous cutting posture variable explanation

[0088]

[0089] Depend on Figure 2 , the instantaneous position of the back face of the milling cutter tooth is:

[0090]

[0091] Among them, G i is the back face equation, G i 0 is the cutting edge equation, M is the transformation matrix from the tooth coordinate system to the workpiece coordinate system, M1 is the translation matrix from the tooth coordinate system to the milling cutter structure coordinate system, M2 is the translation matrix from the cutting coordinate system under vibration to the non-vibration cutting coordinate system, M3 is the translation matrix from the non-vibration cutting coordinate system to the workpiece coordinate system, T1 and T2 are the rotation matrices from the tooth coordinate system to the milling cutter structure coordinate system, T3 is the rotation matrix from the milling cutter structure coordinate system to the cutting coordinate system under vibration, and T4 and T5 are the rotation matrices from the vibration cutting coordinate system to the non-vibration cutting coordinate system.

[0092] Step 2: Calculate the instantaneous position and friction velocity of the blade tooth.

[0093] Depend on Figure 2 And (1), the instantaneous position of the tooth element and its flank face and the instantaneous friction velocity are as follows: Figure 3 As shown:

[0094] Depend on Figure 3 , the instantaneous contact friction characteristic point e1 between the tooth microelement flank surface and the machined transition surface is:

[0095]

[0096] The equation of the common tangent plane at this point Q1(x(t), y(t), z(t)) can be obtained from formula (2), and the instantaneous attitude angle of the tool tooth element in the workpiece coordinate system is obtained as follows:

[0097]

[0098]

[0099] The parametric equation of the tooth flank surface in the workpiece coordinate system is:

[0100]

[0101] Where x Gi (t),y Gi (t),z Gi (t) are the parametric equations of the flank surface of the cutting tooth along the x, y, and z directions respectively.

[0102] According to equations (2) and (5), the motion speed of point e1 on the flank surface of the cutter along the three directions of the workpiece coordinate system is:

[0103]

[0104] Using equations (2) and (6), we can obtain the instantaneous angle β(t) between the normal vector of the common tangent plane at point e1 and the motion velocity v. Then the instantaneous friction velocity v' at point e1 on the flank surface of the tooth element is:

[0105] v'(x(t),y(t),z(t))=-v·sin(π-β(t)) (7)

[0106] According to the above model, in order to solve the instantaneous friction velocity of the flank surface of the cutter tooth, the corresponding milling experiment scheme is shown in Table 2.

[0107] Table 2 Milling experiment parameters

[0108]

[0109]

[0110] The experimental processing site and milling vibration acceleration signal are as follows Figure 4 shown.

[0111] According to the instantaneous friction velocity calculation model of the tooth microelement flank and the vibration acceleration signal of the milling experiment, the tooth velocity in y is calculated. i = 6.7 The dynamic change curve of friction speed is as follows Figure 5 As shown, 0.052s~0.104s is the 1st milling cutter cutting cycle, 7.436s~7.488s is the 143rd milling cutter cutting cycle, 14.924s~14.976 is the 287th milling cutter cutting cycle, 22.360s~22.412s is the 430th milling cutter cutting cycle, and 29.848s~29.900s is the 574th milling cutter cutting cycle.

[0112] As shown in the figure above, the instantaneous friction velocity of the same tooth flank at the same location shows a gradual decrease during each milling cycle, and the moment of cut is significantly greater than the rest of the cutting phase. The results indicate that the cutting load generated by the cutter's cut during milling causes a more dramatic change in the instantaneous contact relationship between the tooth flank and the machined transition surface, further affecting the variation in the instantaneous friction velocity. Milling vibration and tooth error contribute to the varying instantaneous friction velocity of different tooth flanks at the same location.

[0113] Step 3, the calculation method of the instantaneous wear depth of the tool tooth microelement flank;

[0114] The micro-element flank surface and its instantaneous wear depth under the condition of tooth wear are as follows: Figure 4 shown.

[0115] Among them, e1' is the position point of the flank e1 after wear; v hi (t) is the instantaneous wear depth rate measured along the normal vector of the tangent plane at point e1; η1 is the difference between the normal vector of the tangent plane at point e1 and z i Axis space angle; η2 is the normal vector of the tangent plane at point e1 at x i o i y i Projection on the coordinate plane and x i Axis plane angle; Δx i ,Δz i They are respectively the coordinate increments of point e1' relative to e1.

[0116] Depend on Figure 6 The instantaneous growth rate and instantaneous increment of the wear depth of the tooth element flank face measured along the normal vector direction of the common tangent plane at point e1 are:

[0117]

[0118] Where h i (t) is the function of the cumulative wear depth of the flank surface in the thermal-mechanical coupling field of the tooth changing with time.

[0119] Depend on Figure 6 According to formula (8), the instantaneous increment of wear depth causes the tooth edge edge x i and z i The instantaneous increment Δx of the direction i (t), Δz i (t) are:

[0120]

[0121] Where η1 and η2 are the normal vector of the tangent plane at point e1 and z respectively. i 、y iThe instantaneous angle of the axis.

[0122] According to equations (5), (8), and (9), the tooth flank equation under wear conditions is:

[0123]

[0124] From equations (9) to (11), the curve formed by the point where the instantaneous wear depth on the flank surface is 0 is the lower boundary of the instantaneous friction wear on the flank surface of the cutter tooth. At the same time, using equations (1), (8) and (9), the tooth micro-element cutting edge equation under wear conditions and the upper boundary of the instantaneous friction wear on the flank surface of the cutter tooth can be obtained. The solution results of the instantaneous wear boundary of the flank surface of the cutter tooth are as follows: Figure 7 As shown:

[0125] Among them, y i =6.03,y i =6.70,y i =7.37,y i =8.04 is the position where the back face of the tooth is severely worn in the wear area.

[0126] According to the instantaneous wear depth distribution function above, the dynamic change curve of the instantaneous wear depth change rate of different teeth at the same contact angle during the entire milling stroke is obtained as follows: Figure 8 As shown:

[0127] As shown in the figure above, the instantaneous wear depth of the same tooth flank shows a gradually decreasing trend, and the cutting moment is significantly greater than the remaining cutting stages. The results show that during the milling process, the instantaneous wear rate generated by the cutting moment continuously decreases, resulting in a gradual decrease in the degree of wear on the tooth flank, and the wear is more severe in the area closer to the cutting edge.

[0128] Step 4, the instantaneous wear volume calculation method of the tool tooth microelement flank surface;

[0129] According to equations (2) and (8) to (10), using the common tangent surface equation at point e1 and the tooth flank surface equation under wear conditions, the instantaneous friction area ds of the tooth flank surface is solved within the upper and lower boundaries of the instantaneous friction wear of the tooth flank surface. i , then the instantaneous wear volume growth rate V at point e1 on the tooth edge is i (t) and cumulative wear volume ΣV i for:

[0130]

[0131] According to the instantaneous wear volume distribution function, the wear volume distribution of different teeth in the whole milling stroke is 20 μm with the characteristic point as the center at the same contact angle. 2The dynamic change curve of the instantaneous mill volume change rate is as follows: Figure 9 As shown:

[0132] The figure above shows that the instantaneous wear volume at different characteristic points on the same microelement on the tooth flank increases continuously along the tangent vector. Because the area near the cutting edge bears the primary cutting function, frictional wear is most intense near the edge. Within the same cutting cycle, the wear volume at the same point decreases from cut-in to cut-out. This result indicates that the instantaneous contact relationship between the tooth flank and the machined transition surface remains stable during the milling process.

[0133] Step 5, the calculation method of the instantaneous friction energy consumption of the blade tooth microelement flank surface;

[0134] In order to accurately identify the changing characteristics of the friction energy consumption in the instantaneous contact area between the flank surface of the cutter tooth and the machined transition surface, the instantaneous friction force model of the flank surface of the cutter tooth is constructed as follows: Figure 10 shown.

[0135] Depend on Figure 10 , using the equivalent stress of the instantaneous thermal-mechanical coupling field on the flank of the cutter tooth in the workpiece coordinate system, the stress component of the flank of the cutter tooth along the direction of the instantaneous friction velocity is obtained:

[0136] τ i '(t)=σ x (t)cosγ x +σ y (t)cosγ y +σ z (t)cosγ z (12)

[0137] Where, γ x (t), γ y (t), γ z (t), respectively σ x (t), σ y (t), σ z (t) and the angle between it and the friction velocity.

[0138] According to equations (7) and (12), the instantaneous friction energy consumption P at any point on the blade edge is i (t), and the cumulative friction energy consumption ΣE i for:

[0139]

[0140] According to the instantaneous friction energy consumption distribution function, the dynamic change curve of the instantaneous friction energy consumption per unit area of ​​different teeth at the same contact angle during the entire milling stroke is obtained as follows: Figure 11 As shown:

[0141] As shown in the figure above, the instantaneous friction energy consumption at different characteristic points on the same microelement on the tooth flank surface increases first and then decreases from cut-in to cut-out. Its dynamic variation characteristics are similar to the variation characteristics of the instantaneous friction stress on the tooth flank surface. The results show that the instantaneous friction energy consumption on the tooth flank surface is mainly affected by the friction stress. At the same time, the location of the maximum instantaneous friction energy consumption on the tooth flank surface also changes with different instantaneous contact angles, indicating that the location of the tooth flank surface where wear is most severe also changes with different cutting contact angles.

[0142] Step 6: Calculation method of instantaneous friction and wear energy density of the tool tooth microelement flank.

[0143] According to equations (12) and (13), the instantaneous friction and wear energy density e at any point on the tooth flank is i (t), and the average friction and wear energy density during the tooth cutting period for:

[0144]

[0145] Among them, the instantaneous friction wear energy density of the blade tooth microelement back surface is e i (t) represents the instantaneous anti-friction and wear capability of any point on the flank surface. Average friction and wear energy density It indicates the level of resistance to friction and wear at any point on the flank surface during the cutting process.

[0146] According to the instantaneous friction and wear energy density distribution function, the dynamic change curve of the instantaneous friction and wear energy density of different teeth at the same contact angle in the entire milling stroke is obtained as follows: Figure 12 As shown:

[0147] As can be seen from the above figure, the energy density of instantaneous friction and wear on the flank of the cutter tooth is lower in the area near the cutting edge than in the characteristic position of the flank, indicating that the main cutting edge of the cutter tooth is in constant contact with the machining transition surface, resulting in a decrease in its anti-friction and wear energy.

[0148] In order to further analyze the differences in the friction and wear characteristic variables between the teeth, the above results of the friction and wear energy variation characteristics of different teeth were used to select three teeth with the same tooth shape. i =6.70 characteristic point e b1 The results of the difference analysis are as follows Figure 13 As shown:

[0149] Figure 13 In, T1=0.052s~0.104s, T2=7.436s~7.488s, T3=14.924s~14.976s, T4=22.360s~22.412s, T5=29.848~29.00s, is the average friction and wear energy density of a milling cutter cutting cycle, e imin is the minimum friction and wear energy density of a milling cutter cutting cycle, e imax is the maximum value of friction and wear energy density during a milling cutter cutting cycle, ∑E i is the cumulative friction energy consumption of a milling cutter cutting cycle.

[0150] Depend on Figure 13 It can be seen that the friction and wear energy density of tooth 1 has the smallest range of variation, its average friction and wear energy density is much higher than that of the other two teeth, and the cumulative friction energy consumption of tooth 1 is the lowest. This shows that tooth 1 has a higher resistance to friction and wear than the other two teeth.

[0151] The friction wear characteristic parameters such as the maximum, minimum, average and cumulative friction energy consumption of the tooth flank friction wear energy density in a milling cutter cutting cycle are used to compare and analyze the friction wear differences at different positions on the tooth flank of the milling cutter. Among them, the friction wear comparison analysis results of different positions on the three tooth flanks of the milling cutter in the 287th milling cutter cutting cycle are as follows: Figure 14 shown.

[0152] Among them, e a1 、e a2 、e a3 、e a4 、e a5 For 3 teeth in y i = 5 feature points at 6.03, e b1 、e b2 、e b3 、e b4 、e b5 For 3 teeth in y i = 5 feature points at 6.70, e c1 、e c2 、e c3 、e c4 、e c5 For 3 teeth in y i = 5 feature points at 7.37, e d1 、e d2 、e d3 、e d4 、e d5 For 3 teeth in y i = 5 feature points at 8.04.

[0153] The results show that the closer to the cutting edge, the lower the characteristic parameters of friction and wear energy density, and the higher the cumulative friction energy consumption, indicating that the closer to the cutting edge, the worse the anti-friction and wear ability.

[0154] In order to verify the accuracy of the calculation model of instantaneous friction wear energy density of the tooth flank, according to the results of the high feed milling cutter cutting experiment, the tooth flank is i = 6.70 The cumulative wear depth solution result is as follows Figure 15 As shown:

[0155] The significance analysis was conducted between the cumulative wear depth under the experimental scheme and the inverse of the maximum energy density, the inverse of the minimum energy density, the inverse of the average energy density and the cumulative friction energy consumption. The results are as follows: Figure 16 As shown:

[0156] The results show that the closer to the cutting edge, the higher the cumulative friction energy consumption, and the more significant the cumulative wear depth obtained experimentally. The inverse of the average energy density is positively correlated with the cumulative wear depth, and the inverse of the maximum energy density is positively correlated with the cumulative wear depth, and the above values ​​increase the closer to the cutting edge.

[0157] The above experimental results show that the method for calculating the instantaneous friction and wear energy density of the flank surface of the high-feed milling cutter tooth constructed by the present invention is accurate.

[0158] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutations and combinations. Therefore, the present invention will no longer describe the technical solutions after permutations and combinations one by one, but it should be understood that the technical solutions after permutations and combinations have been disclosed by the present invention.

[0159] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for identifying the changing characteristics of instantaneous friction and wear energy density of the flank face of a high-efficiency milling cutter, characterized in that: include: Step 1, the instantaneous pose calculation method of the flank of the milling cutter teeth; Step 2: Calculate the instantaneous position and friction velocity of the blade tooth. Step 3, the calculation method of the instantaneous wear depth of the tool tooth microelement flank; Step 4, the instantaneous wear volume calculation method of the tool tooth microelement flank surface; Step 5, the calculation method of the instantaneous friction energy consumption of the blade tooth microelement flank surface; Step 6, a method for calculating the instantaneous friction and wear energy density of the tool tooth microelement flank surface; The step 1 includes: determining a milling processing mode, determining the milling cutter and its tooth structure parameters and cutting parameters, and performing milling cutter trajectory and instantaneous posture solution and tooth microelement instantaneous posture solution under the action of milling vibration signal, that is, obtaining the high feed milling cutter structure and the instantaneous cutting posture of the milling cutter and tooth under the action of vibration; The instantaneous posture of the flank face and cutting edge of the cutter tooth is: (1) In the formula, o-xyz is the workpiece coordinate system, point o is the intersection of the bottom, back and right vertical surfaces of the workpiece, the x-axis is in the same direction as the milling cutter feed direction, the y-axis is in the same direction as the workpiece cutting width direction, and the z-axis is in the same direction as the workpiece cutting depth direction. i -x i y i z i The tooth coordinate system is the cutting edge abe o The projection to the bottom surface is b1-e o ´-a1, over e o Draw a tangent to the bottom surface and draw a perpendicular line through b1, the intersection of which is the origin o i , o i e o ´Direction is y i Axis oi b1 is z i Axis, perpendicular to the bottom axis is x i Axis, G i is the back face equation, G i 0 is the cutting edge equation, M is the transformation matrix from the tooth coordinate system to the workpiece coordinate system, M1 is the translation matrix from the tooth coordinate system to the milling cutter structure coordinate system, M2 is the translation matrix from the cutting coordinate system under vibration to the non-vibration cutting coordinate system, M3 is the translation matrix from the non-vibration cutting coordinate system to the workpiece coordinate system, T1 and T2 are the rotation matrices from the tooth coordinate system to the milling cutter structure coordinate system, T3 is the rotation matrix from the milling cutter structure coordinate system to the cutting coordinate system under vibration, and T4 and T5 are the rotation matrices from the vibration cutting coordinate system to the non-vibration cutting coordinate system.

2. The method for identifying the changing characteristics of the instantaneous friction and wear energy density of the flank face of a high-efficiency milling cutter according to claim 1 is characterized in that: The step 2 includes: Obtain the instantaneous position and friction velocity of the tooth element and its flank surface; The instantaneous contact friction characteristic point e1 between the tooth microelement flank face and the machined transition surface is calculated as: (2) The common tangent plane equation Q1(x(t), y(t), z(t)=0) is obtained from formula (2), and the instantaneous attitude angle of the tool tooth element in the workpiece coordinate system is obtained as follows: (3) (4) The parametric equation of the tooth flank surface in the workpiece coordinate system is: (5) Where x Gi (t), y Gi (t), z Gi (t) are the parametric equations of the flank surface of the cutter along the x, y, and z directions respectively; According to equations (2) and (5), the motion speed of point e1 on the flank surface of the cutter along the three directions of the workpiece coordinate system is: ， ， (6) Using equations (2) and (6), we can obtain the instantaneous angle β(t) between the normal vector of the common tangent plane at point e1 and the motion velocity v(t). Then, the instantaneous friction velocity v'(t) at point e1 on the flank surface of the tooth element is: (7)。 3. The method for identifying the changing characteristics of the instantaneous friction and wear energy density of the flank face of a high-efficiency milling cutter according to claim 2, characterized in that: The step 3 includes: Obtain the micro-element flank surface and its instantaneous wear depth under the condition of tooth wear, e1' is the position point of the flank surface after point e1 is worn; v hi (t) is the instantaneous wear depth rate measured along the normal vector of the tangent plane at point e1; η1 is the difference between the normal vector of the tangent plane at point e1 and z i Axis space angle; η2 is the normal vector of the tangent plane at point e1 at x i o i y i Projection on the coordinate plane and x i Axis plane angle; Δx i , Δz i are the coordinate increments of point e1' relative to e1; The instantaneous growth rate and instantaneous increment of the wear depth of the tooth element flank face measured along the normal vector direction of the common tangent plane at point e1 are: ， (8) Where h i (t) is the cumulative wear depth of the flank surface in the thermal-mechanical coupling field of the cutter tooth as a function of time; The instantaneous increase in wear depth causes the tooth edge of the tool to i and z i The instantaneous increment Δx of the direction i (t), Δz i (t) are: (9) Where η1 and η2 are the normal vector of the tangent plane at point e1 and z respectively. i 、y i The instantaneous angle of the axis; According to equations (5), (8), and (9), the equation for calculating the tooth flank surface under wear conditions is: (10) According to equations (9) to (11), the curve formed by the point where the instantaneous wear depth on the flank surface is 0 is the lower boundary of the instantaneous friction wear on the flank surface of the cutter tooth. At the same time, using equations (1), (8) and (9), the tooth micro-element cutting edge equation under wear conditions and the upper boundary of the instantaneous friction wear on the flank surface of the cutter tooth are obtained.

4. The method for identifying the changing characteristics of the instantaneous friction and wear energy density of the flank face of a high-efficiency milling cutter according to claim 3 is characterized by: The step 4 comprises: According to equations (2) and (8) to (10), using the common tangent surface equation at point e1 and the tooth infinitesimal flank surface equation under wear conditions, the instantaneous friction area s of the tooth infinitesimal flank surface is solved within the upper and lower boundaries of the instantaneous friction wear of the tooth flank surface. i , then the instantaneous wear volume growth rate V at point e1 on the tooth edge is i (t) and cumulative wear volume ΣV i for: (11) Where L is the boundary of the instantaneous friction area at point e1 on the flank surface of the tooth.

5. The method for identifying the changing characteristics of the instantaneous friction and wear energy density of the flank face of a high-efficiency milling cutter according to claim 4, characterized in that: The step 5 comprises: In order to accurately identify the changing characteristics of the friction energy consumption in the instantaneous contact area between the tooth flank and the machined transition surface, a transient friction stress model of the tooth flank was constructed. Using the equivalent stress of the instantaneous thermal-mechanical coupling field on the flank surface of the cutter tooth in the workpiece coordinate system, the stress component along the instantaneous friction velocity direction of the flank surface of the cutter tooth microelement is obtained as follows: （12） Where, γ x (t), γ y (t), γ z (t), respectively σ x (t), σ y (t), σ z (t) The angle between it and the friction speed; According to equations (7) and (12), the instantaneous friction energy consumption P at any point on the blade edge is i (t), and the cumulative friction energy consumption ΣE i for: ， （13） Where, t j , t j+1 They are the start time and end time of tooth cutting respectively.

6. The method for identifying the changing characteristics of the instantaneous friction and wear energy density of the flank face of a high-efficiency milling cutter according to claim 5, characterized in that: The step 6 comprises: According to equations (12) and (13), the instantaneous friction and wear energy density e at any point on the blade edge is i (t), and the average friction and wear energy density during the tooth cutting period for: ， (14) Where, the instantaneous friction wear energy density e of the blade tooth microelement flank is i (t), represents the instantaneous anti-friction and wear capability of the flank surface; average friction and wear energy density , which indicates the level of resistance to friction and wear of the back face of the tooth element during the cutting process.

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