Modeling and cutting force coefficient and run-out parameter identification method for annular cutter

Abstract

The invention relates to the field of intelligent machining, in particular to a modeling and cutting force coefficient and run-out parameter identification method for an annular cutter, which comprises the following steps of: S1, performing dynamic cutting force accurate modeling of the annular cutter; the method specifically comprises the steps of geometric modeling of the annular cutter, modeling of infinitesimal contact, modeling of instantaneous undeformed cutting thickness, modeling of dynamic cutting thickness and modeling of dynamic cutting force. S2, accurately and efficiently identifying a cutting force coefficient and a run-out parameter of the annular cutter; the method specifically comprises the steps of implementing a mechanical identification method and optimizing an identification method. According to the method, the variable geometry annular cutter with a more complex geometric structure and higher universality is selected as a modeling object, complex working conditions on site are fully considered, multiple regeneration effects are introduced into the modeling process, a cutting force model can be more accurate, and theoretical support is provided for site process parameter selection.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent machining, in particular to a modeling and cutting force coefficient and run-out parameter identification method for a ring-shaped cutter. BACKGROUND

[0002] With the continuous development of aviation technology, higher requirements are put forward for product performance, and the trend of overallization and thinning of parts is more obvious, which not only can reduce the number of parts and effectively reduce the cost, but also can achieve the purpose of weight reduction of the aircraft. However, during the machining of such parts, due to unreasonable selection of cutting parameters, it is easy to cause excessive cutting force and lead to machining instability problems such as machining deformation or cutting chatter, which affects the machining quality and efficiency of the parts.

[0003] In order to effectively control the machining instability, the cutting parameters are usually adjusted by continuously trying to cut in the field, so as to achieve the purpose of changing the size of the cutting force. Such method not only takes a long time, but also has high cost and poor reliability. The reason is that there is no related cutting force accurate model in the field, and the size of the cutting force of the related parameters cannot be predicted in advance. In the cutting force model, the cutting force coefficient is a key factor affecting the modeling of the cutting force. If the identification is not accurate, it will directly affect the accuracy of the size of the cutting force.

[0004] In actual production field, when the aircraft structure is machined, the ring-shaped cutter is a commonly used milling cutter. Since the structure of such cutter is more complex compared with the common ball head cutter and end milling cutter, the geometric radius, helix angle, contact angle, lag angle and the like vary along different positions of the cutter shaft. In addition, due to the existence of cutter run-out in the actual machining process, the multiple regenerative effect is more obvious, which brings great challenge to the cutting force modeling. For the conventional cutting force modeling and coefficient identification method, it is difficult to accurately be used for accurate force prediction of such cutter. Therefore, it is of great significance to propose an accurate and efficient identification method for the accurate modeling of the cutting force of the ring-shaped cutter and the cutting force coefficient and run-out parameter. SUMMARY

[0005] To solve the above problems, the present application provides a modeling and cutting force coefficient and run-out parameter identification method for a ring-shaped cutter.

[0006] In order to achieve the above application purpose, the technical scheme provided by the present application is as follows: A modeling and cutting force coefficient and run-out parameter identification method for a ring-shaped cutter, comprising the following steps: Step S1. Dynamic cutting force accurate modeling of the ring-shaped cutter is performed. Specifically, it comprises geometric modeling of the ring-shaped cutter, micro-element contact modeling, instantaneous undeformed cutting thickness modeling, dynamic cutting thickness modeling and dynamic cutting force modeling. Step S2. Accurately and efficiently identify the cutting force coefficient and runout parameter of the ring cutter; Specifically, the mechanical identification method and the optimized identification method are implemented.

[0007] Further, in the ring cutter geometry modeling, the ring cutter geometry model is a variable geometry cutter with variable pitch and variable helix angle to make the modeling more general. Further, in the ring cutter geometry modeling, the blade of the cutter geometry model is composed of a circular arc part and a cylindrical part, the cutter radius changes along the axial direction, specifically: (1) In the formula, is the radius varying with the axial direction of the cutter, D is the diameter of the cylindrical part, R is the radius of the circular arc part, and z is the axial height based on the bottom of the cutter circular arc.

[0008] Further, in the ring cutter geometry modeling, the axial contact angle of the cutter varies with the axial height, specifically: (2) In the formula, is the axial contact angle varying with the axial direction of the cutter.

[0009] Further, in the ring cutter geometry modeling, the helix angle of the cutter varies with the axial height, specifically: (3) In the formula, is the helix angle of the kth tooth varying with the axial direction of the cutter, is the helix angle of the kth tooth at the axial height of the value R (i.e. the cylindrical part).

[0010] Further, in the ring cutter geometry modeling, the radial contact angle of the cutter varies with the axial height, specifically: (4) In the formula, is the radial contact angle of the kth tooth varying with the axial direction of the cutter, is the position angle of the reference tooth (the 1st tooth) at the axial height of 0, is the tooth pitch angle of the kth tooth and the reference tooth at the axial height of 0, is the lag angle of the kth tooth at the axial height z, is the main shaft speed, and t is time.

[0011] Further, in the ring cutter geometry modeling, the cutter lag angle varies with the axial height, specifically: (5) In the formula, Let be the hysteresis angle of the k-th tooth as it changes with the tool axis.

[0012] Furthermore, in the geometric modeling of the ring cutter, the expression for calculating the tooth pitch angle is: (6) In the formula, Let be the tooth pitch angle between the k-th tooth and the (k-1)-th tooth as a function of axial height under the influence of tool runout. and These represent the actual cutting radii of the (k-1)th and kth teeth at the axial height z, respectively, affected by tool runout. Let z be the distance between the tips of the (k-1)th and kth teeth at the axial height z.

[0013] Furthermore, in the geometric modeling of the ring cutter, for a cutter with a constant helix angle, its tooth pitch angle remains constant, while for a cutter with a variable helix angle, its tooth pitch angle changes depending on the axial height, specifically as follows: (7) In the formula, Let be the tooth pitch angle between the k-th and (k-1)-th teeth of the cutting tool as a function of axial height. The pitch angle is the angle between the k-th tooth and the (k-1)-th tooth at the junction of the arc and cylindrical parts of the cutting tool.

[0014] Furthermore, in the geometric modeling of the ring cutter, under the influence of tool runout, the actual cutting radius expression is: (8) In the formula, This represents the tool runout offset. It varies with the axial height, specifically as follows: (9) In the formula, The runout position angle at the axial height R is [value missing]. Let be the tooth pitch angle at z for the k-th tooth and the reference tooth.

[0015] Furthermore, in the aforementioned micro-element contact modeling, during the cutting process, the radial depth of cut changes with the axial height, specifically as follows: (10) In the formula, The radial depth of cut varies with the tool axis. This is the nominal radial depth of cut.

[0016] Furthermore, in the micro-element contact modeling, the expression for the feed per tooth under the influence of tool runout is: (11) In the formula, is the feed per tooth for the kth tooth, is the average value of the feed per tooth, and N is the number of teeth.

[0017] Further, in the micro-element contact modeling, under the influence of tool runout, when the tool is engaged in climb milling, the expressions of the entry angle and the exit angle are: Entry angle: (12) Exit angle: (13) wherein, is the multiple regeneration index, , satisfies the following relationship: (14) When the tool is engaged in down milling, the entry angle is: (15)The exit angle is: (16).

[0018] Further, in the micro-element contact modeling, the unit step function is used to determine whether the tool tooth is cutting the workpiece, and the expression is: (17).

[0019] Further, in the instantaneous undeformed cut thickness modeling, under the influence of multiple regeneration effects, the expression of the cut thickness is: (18).

[0020] Further, in the instantaneous undeformed cut thickness modeling, under the influence of runout, when the phenomenon of tooth skipping occurs, the expression is: (19).

[0021] Further, in the dynamic cut thickness modeling, the instantaneous undeformed cut thickness includes static cut thickness and dynamic cut thickness, and the expression is: (20) wherein, is the static cut thickness, is the dynamic cut thickness.

[0022] Further, in the dynamic cut thickness modeling, the expression of the static cut thickness under the influence of multiple regeneration effects is: (21).

[0023] Further, in the dynamic cut thickness modeling, the expression of the dynamic cut thickness under the influence of multiple regeneration effects is: (22) where, , , are the vibration of the tool in three directions under the current tooth period, , , are the vibration of the workpiece in three directions under the current tooth period, , , are the vibration of the tool in three directions under the multiple regeneration effects, , , are the vibration of the workpiece in three directions under the multiple regeneration effects.

[0024] Further, in the dynamic cutting force modeling, the expression of the dynamic cutting force acting on the mth axial cutting microelement of the kth cutting edge of the tool at time t is: (23) where, , , are the cutting force coefficients in the tangential, radial and axial directions, respectively.

[0025] Further, in the dynamic cutting force modeling, in the tool coordinate system, the microelement cutting force is decomposed into forces along the x, y and z directions, specifically: (24).

[0026] Further, in the dynamic cutting force modeling, all microelement cutting forces are accumulated to obtain the expression of the total cutting force of the tool: (25) where, is the discrete number of the tool along the axial direction.

[0027] Further, in the mechanical identification method, without considering the tool runout, the average processing of the cutting force per tooth is expressed as: (26) where, , represent the entry and exit angles, respectively.

[0028] Further, in the mechanical identification method, the cutting force measurement value is obtained through experiments, and the specific expression is obtained by using linear regression processing: (27) where, , respectively, are shear force and edge force.

[0029] Further, in the mechanical identification method, based on the obtained theoretical average cutting force and experimental measurement value, the cutting force coefficient expression is: (28) (29) (30) (31) (32) (33) wherein, , , the expression of is: (34) (35) (36) Further, in the mechanical identification method, the preliminary identification of the cutting force can be achieved by the method, but the run-out parameter cannot be identified, and further optimization identification method is needed to achieve.

[0030] In the optimization identification method, the theoretical prediction value is corresponded with the experimental measurement value, and the expression is: (37) wherein, , , respectively, are theoretical prediction values in three directions, , , respectively, are experimental measurement values in three directions.

[0031] Further, in the optimization identification method, the theoretical prediction value is divided into S parts within one rotation of the tool, and is expressed as: (38).

[0032] Further, in the optimization identification method, the theoretical cutting force expression is: (39).

[0034] Further, in the optimization identification method, the experimental measurement value under the steady-state cutting condition is expressed as: (40) wherein, is the experimental sampling period, and n is a positive integer.

[0035] Further, in the optimization identification method, the corresponding relation equation between the theoretical prediction value and the experimental measurement value is a nonlinear overdetermined equation group, which is converted into a nonlinear optimization problem, and the expression is: (41) wherein, is the cutting force data selected at equal intervals in the experimental measurement value.

[0036] Further, in the optimization identification method, when solving , without any derivative information, the cutting force coefficient and the runout parameter are synchronously identified by using the unconstrained nonlinear programming function Fminsearch, the optimized value is constantly updated by using the Nelder-Mead algorithm in the identification process, and the objective function is minimized under the condition of meeting the iteration tolerance.

[0037] The present application has the following advantages: 1. The present application can accurately model the cutting force in the cutting process of the variable geometry ring-shaped cutter under complex working conditions and synchronously and accurately identify the cutting force coefficient and the runout parameter, on the basis of which, the rationality of the machining parameters is predicted through the cutting force size prediction, the reliability of the on-site part machining is effectively ensured, and the high-performance machining of the thin-walled part is realized.

[0038] 2. The present application selects the variable geometry ring-shaped cutter with more complex geometric structure and more universality as the modeling object, fully considers the complex working conditions on site, introduces multiple regenerative effects into the modeling process, can make the cutting force model more accurate, and provides theoretical support for on-site process parameter selection.

[0039] 3. The present application comprehensively uses the mechanical identification method and the optimization identification method, preliminarily obtains the cutting force coefficient through the mechanical identification method, locks the optimization range in advance for the optimization identification method, and identifies the cutting force coefficient and the runout parameter at one time through the optimization identification method, without distribution, which greatly reduces the optimization calculation time, not only has high identification accuracy, but also significantly improves the calculation efficiency. 4. The cutting force modeling and cutting force coefficient identification method provided by the present application is not only suitable for variable geometry milling cutters, but also suitable for conventional general milling cutters, has strong universality, and has wide application range. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is the cutting force coefficient and runout parameter identification process.

[0041] Figure 2Figure for comparison of results of mechanical identification method of variable geometry ring cutter (comparison of simulation value and measured value in x direction).

[0042] Figure 3 Figure for comparison of results of mechanical identification method of variable geometry ring cutter (comparison of simulation value and measured value in y direction).

[0043] Figure 4 Figure for comparison of results of mechanical identification method of variable geometry ring cutter (comparison of simulation value and measured value in z direction).

[0044] Figure 5 Figure for comparison of results of optimized identification method of variable geometry ring cutter (comparison of simulation value and measured value in x direction).

[0045] Figure 6 Figure for comparison of results of optimized identification method of variable geometry ring cutter (comparison of simulation value and measured value in y direction).

[0046] Figure 7 Figure for comparison of results of optimized identification method of variable geometry ring cutter (comparison of simulation value and measured value in z direction).

[0047] Figure 8 Figure for comparison of results of optimized identification method of conventional end mill (comparison of simulation value and measured value in x direction).

[0048] Figure 9 Figure for comparison of results of optimized identification method of conventional end mill (comparison of simulation value and measured value in y direction).

[0049] Figure 10 Figure for comparison of results of optimized identification method of conventional end mill (comparison of simulation value and measured value in z direction). DETAILED DESCRIPTION

[0050] In order to make the objectives, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are used to explain the present application but not to limit the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0051] The specific implementation methods of the present application are described below in combination with the drawings and examples, and the present application is not limited to the embodiments.

[0052] Embodiment 1 A modeling and cutting force coefficient and run-out parameter identification method for a ring cutter, comprising the following steps: Step S1. performing dynamic cutting force accurate modeling of the ring cutter; Specifically, the ring cutter geometry modeling, microelement contact modeling, instantaneous undeformed cut thickness modeling, dynamic cut thickness modeling and dynamic cutting force modeling are included. Step S2. Accurate and efficient identification of ring cutter cutting force coefficients and runout parameters; Specifically, the mechanical identification method and the optimization identification method are implemented.

[0053] Further, in the ring cutter geometry modeling, in order to make the modeling more general, the ring cutter geometry model is a variable geometry milling cutter with variable pitch and variable helix angle. Further, in the ring cutter geometry modeling, the blade of the cutter geometry model is composed of a circular arc part and a cylindrical part, the cutter radius changes along the axial direction, specifically: (1) In the formula, is the radius varying with the axial direction of the cutter, D is the diameter of the cylindrical part, R is the fillet radius of the circular arc part, and z is the axial height based on the bottom of the cutter circular arc.

[0054] Further, in the ring cutter geometry modeling, the axial contact angle of the cutter varies with the axial height, specifically: (2) In the formula, is the axial contact angle varying with the axial direction of the cutter.

[0055] Further, in the ring cutter geometry modeling, the helix angle of the cutter varies with the axial height, specifically: (3) In the formula, is the helix angle of the kth tooth varying with the axial direction of the cutter, is the helix angle of the kth tooth at the axial height of the value R (i.e. the cylindrical part).

[0056] Further, in the ring cutter geometry modeling, the radial contact angle of the cutter varies with the axial height, specifically: (4) In the formula, is the radial contact angle of the kth tooth varying with the axial direction of the cutter, is the position angle of the reference tooth (the 1st tooth) at the axial height of 0, is the tooth pitch angle of the kth tooth and the reference tooth at the axial height of 0, is the lag angle of the kth tooth at the axial height z, is the spindle speed, and t is time.

[0057] Further, in the ring cutter geometry modeling, the lag angle of the cutter varies with the axial height, specifically: (5) where, is the lag angle of the kth tooth with respect to the axial direction of the tool.

[0058] Further, in the modeling of the ring tool geometry, the expression of the tooth spacing angle is: (6) where, is the tooth spacing angle of the kth tooth and the (k-1)th tooth with respect to the axial height under the influence of tool runout, and are the actual tool cutting radius of the (k-1)th tooth and the kth tooth at the axial height z under the influence of tool runout, respectively, is the distance between the two tooth tips of the (k-1)th tooth and the kth tooth at the axial height z.

[0059] Further, in the modeling of the ring tool geometry, for the equal helix angle tool, the tooth spacing angle is constant, while for the variable helix angle tool, the tooth spacing angle changes with the axial height, specifically: (7) where, is the tooth spacing angle of the kth tooth and the (k-1)th tooth with respect to the axial height, is the tooth spacing angle between the kth tooth and the (k-1)th tooth at the intersection of the circular arc and the cylindrical part of the tool.

[0060] Further, in the modeling of the ring tool geometry, under the influence of tool runout, the expression of the actual cutting radius is: (8) where, is the tool runout offset, changes with the axial height, specifically: (9) where, is the runout position angle at the axial height R, is the tooth spacing angle of the kth tooth and the reference tooth at z.

[0061] Further, in the modeling of the micro-element contact, when the radial depth of cut changes with the axial height during the cutting process, specifically: (10) where, is the radial depth of cut with respect to the axial direction of the tool, is the nominal radial depth of cut.

[0062] Further, in the micro-element contact modeling, the expression of the feed per tooth under the influence of tool runout is: (11) wherein, is the feed per tooth of the kth tooth, is the average value of the feed per tooth, and N is the number of teeth.

[0063] Further, in the micro-element contact modeling, the expressions of the entry and exit angles when finishing under the influence of tool runout are: Entry angle: (12) Exit angle: (13) wherein, is the multiple regeneration index, , satisfies the following relationship: (14) When finishing, the entry angle is: (15)The exit angle is: (16).

[0064] Further, in the micro-element contact modeling, the unit step function is used to determine whether the tooth cuts the workpiece, and the expression is: (17).

[0065] Further, in the instantaneous undeformed cut thickness modeling, the expression of the cut thickness under the influence of multiple regeneration effects is: (18).

[0066] Further, in the instantaneous undeformed cut thickness modeling, the expression when the tooth jump phenomenon occurs under the influence of runout is: (19).

[0067] Further, in the dynamic cut thickness modeling, the instantaneous undeformed cut thickness includes static cut thickness and dynamic cut thickness, and the expression is: (20) wherein, is the static cut thickness, is the dynamic cut thickness.

[0068] Further, in the dynamic cut thickness modeling, the expression of the static cut thickness under the influence of multiple regeneration effects is: (21).

[0069] Further, in the dynamic cutting thickness modeling, the dynamic cutting thickness expression under the multiple regeneration effects is: (22) wherein, , , are the vibrations of the tool in three directions under the current tooth period, , , are the vibrations of the workpiece in three directions under the current tooth period, , , are the vibrations of the tool in three directions under the multiple regeneration effects, , , are the vibrations of the workpiece in three directions under the multiple regeneration effects.

[0070] Further, in the dynamic cutting force modeling, the dynamic cutting force expression of the micro element of the kth cutting edge of the tool in the mth axial direction at t time is: (23) wherein, , , are the cutting force coefficients in the tangential direction, the radial direction and the axial direction.

[0071] Further, in the dynamic cutting force modeling, in the tool coordinate system, the micro element cutting force is decomposed into forces along x, y and z three directions, specifically: (24).

[0072] Further, in the dynamic cutting force modeling, all the micro element cutting forces are accumulated, and the total cutting force expression of the tool is: (25) wherein, is the discrete number of the tool along the axial direction.

[0073] Further, in the mechanical identification method, when the tool runout is not considered, the average processing of the cutting force per tooth is expressed as: (26) wherein, , respectively represent the entry angle and the exit angle.

[0074] Further, in the mechanical identification method, the cutting force measurement value is obtained through experiment, and a specific expression is obtained by linear regression processing: (27) In the formula, , are shear force and edge force, respectively.

[0075] Further, in the mechanical identification method, based on the obtained theoretical average cutting force and experimental measurement value, the cutting force coefficient expression is: (28) (29) (30) (31) (32) (33) In the formula, , , The expression of is: (34) (35) (36) Further, in the mechanical identification method, the preliminary identification of the cutting force can be achieved by this method, but the run-out parameter cannot be identified, and further optimization identification method is needed to achieve.

[0076] In the optimization identification method, the theoretical prediction value is corresponded with the experimental measurement value, and the expression is: (37) In the formula, , , are theoretical prediction values in three directions, respectively, , , are experimental measurement values in three directions, respectively.

[0077] Further, in the optimization identification method, the theoretical prediction value is divided into S parts within one revolution of the tool, and is expressed as: (38).

[0078] Further, in the optimization identification method, the theoretical cutting force expression is: (39).

[0080] Further, in the optimization identification method, the experimental measurement value under the steady cutting condition is expressed as: (40) In the formula, is the experimental sampling period, and n is a positive integer.

[0081] Further, in the optimization identification method, since the corresponding relationship equation between the theoretical prediction value and the experimental measurement value is a nonlinear overdetermined equation group, it is converted into a nonlinear optimization problem, and the expression is: (41) In the formula, is the cutting force data selected at equal intervals in the experimental measurement value.

[0082] Further, in the optimization identification method, when solving , without any derivative information, the cutting force coefficient and the runout parameter are simultaneously identified by using the unconstrained nonlinear programming function Fminsearch, and the Nelder-Mead algorithm is used to update the optimized value in the identification process, so that the objective function is minimized under the condition of meeting the iteration tolerance.

[0083] Example 2 The application provides a modeling and cutting force coefficient and runout parameter identification method for a ring-shaped cutter, which includes accurate modeling of dynamic cutting force of the ring-shaped cutter and accurate and efficient identification of cutting force coefficients and runout parameters of the ring-shaped cutter. The accurate modeling of the dynamic cutting force of the ring-shaped cutter includes geometric modeling of the ring-shaped cutter, micro-element contact modeling, instantaneous undeformed cutting thickness modeling, dynamic cutting thickness modeling, and dynamic cutting force modeling. On this basis, the cutting force coefficients and the runout parameters need to be further identified.

[0084] The accurate and efficient identification of the cutting force coefficients and the runout parameters of the ring-shaped cutter includes a mechanical identification method and an optimization identification method, and the specific process is as shown in Figure 1 , and the steps are as follows: Step 1: initialization of the cutting force coefficient and the runout parameter. The initial value of the cutting force coefficient can be obtained by the mechanical identification method, and the initial value of the runout parameter can be given according to experience.

[0085] Step 2: boundary value determination. The cutting force coefficient and the runout parameter in step 1 are multiplied by a boundary factor, respectively, wherein the upper boundary factor is less than 1, and the lower boundary factor is greater than 1.

[0086] Step 3: calculation of the theoretical cutting force. The theoretical value of the cutting force is obtained based on formula (39).

[0087] Step 4: Objective function optimization solution. Combine the theoretical value calculated in step 2 with the measured value, construct the objective function according to formula (41), set the tolerance, and then use the optimization algorithm to solve it iteratively. Finally, the cutting force coefficient and run-out parameter are identified simultaneously.

[0088] Example 3 Select variable geometry ring cutter to cut 45 steel to identify cutting force coefficient and run-out parameter simultaneously.

[0089] The selected tool parameters are: diameter 20mm, number of teeth 4, corner radius 4mm, helix angle 48°, tooth spacing angle 87.5-92.5-87.5-92.5°, tool length 100mm, maximum cutting depth 45mm.

[0090] During the cutting process of the ring cutter, the influence of tool size effect should be fully considered. The milling method is groove milling, the speed is 2000rpm, the axial cutting is 5, the axial cutting is 0.4, 0.8, 1.2, 1.6, 2.0mm, and the feed per tooth is 0.005, 0.01, 0.015, 0.02mm / tooth.

[0091] Based on the above experimental scheme, Kistler dynamometer is used to collect cutting force data. The average force in three directions is shown in Table 1.

[0092] Table 1 Average cutting force under different cutting parameters

[0093] Based on the above experimental force value, the relationship expression of cutting force in three directions with axial depth of cut can be obtained by mechanical identification method: (42) Select spindle speed 2000rpm, axial depth of cut 0.4mm, radial depth of cut 20mm, feed per tooth 0.015mm / tooth to compare the predicted value with the measured value, the result is shown in Figures 2-4 From the figure, it can be found that there is a big difference between the predicted value and the measured value, which shows that the influence of tool run-out is great.

[0094] Therefore, further identification is carried out by optimization identification method for the same cutting parameters as above, and the result is: 、 、 、 、 、 、 、 . Bring it into the theoretical cutting force model and compare it with the measured value, the result isFigures 5-7 Theoretical prediction values and experimental measurement values are in good agreement and can better reflect the actual cutting conditions.

[0095] Example 4 The conventional end mill is selected to cut aluminum alloy for verification, and this combination is more common, which is a typical verification type. The size of the end mill is: diameter 20 mm, number of teeth 3, helix angle 45°, tool length 100 mm, and maximum cutting depth 45 mm. The same identification process as in the example is adopted, which is not described here. The obtained identification result is: The obtained identification result is brought into the theoretical model and compared with the measured value, and the obtained result is shown in Figures 8-10 . The cutting conditions are: spindle speed 3000 rpm, axial cutting depth 4 mm, radial cutting depth 2 mm, feed per tooth 0.05 mm / tooth, and milling method is down milling. It can be seen from the figure that the theoretical cutting force and the experimental measurement value are in good agreement.

[0096] From the above example analysis, it can be seen that the cutting force accurate modeling and cutting force coefficient and synchronous precise identification method of the jump parameters can accurately predict the cutting force of the variable geometry milling cutter with complex geometric structure, and can accurately predict the cutting force of the conventional cutter with simple structure, which can meet the process parameter optimization demand based on the size of the cutting force in the actual production site.​​​​​​​

Claims

1. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter, characterized in that, Includes the following steps: Step S1. Perform accurate modeling of the dynamic cutting force of the ring cutter; Specifically, this includes geometric modeling of the ring cutter, contact modeling of micro-elements, modeling of instantaneous undeformed cutting thickness, modeling of dynamic cutting thickness, and modeling of dynamic cutting force; Step S2. Accurately and efficiently identify the cutting force coefficient and runout parameters of the ring cutter; Specifically, this includes implementing mechanical identification methods and optimized identification methods.

2. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 1, characterized in that, In the geometric modeling of the ring cutter, the geometric model of the ring cutter is a variable geometry milling cutter with variable tooth pitch / variable helix angle.

3. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 2, characterized in that, In the geometric modeling of the ring cutter, the cutting edge of the tool geometry model consists of an arc portion and a cylindrical portion, and its tool radius varies along the axial direction, specifically as follows: （1） In the formula, The radius varies with the tool axis, D is the diameter of the cylindrical part, R is the fillet radius of the arc part, and z is the axial height with the bottom of the tool arc as the reference. In the geometric modeling of the ring cutter, the axial contact angle of the tool varies with the axial height, specifically as follows: （2） In the formula, This is the axial contact angle that varies with the tool axis.

4. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 3, characterized in that, In the geometric modeling of the ring cutter, the helix angle of the cutter varies with the axial height, specifically as follows: （3） In the formula, Let be the helix angle of the k-th tooth as it varies with the tool axis. Let R be the helix angle of the k-th tooth at an axial height of value R; The radial contact angle of the tool varies with the axial height, specifically as follows: （4） In the formula, Let $\frac{k}{k}$ be the radial contact angle of the $k$ tooth as it varies with the tool axis. The reference tooth's position angle at an axial height of 0. Let be the tooth pitch angle between the k-th tooth and the reference tooth at axial height 0. Let be the hysteresis angle of the k-th tooth at the axial height z. t is the spindle speed, and t is time.

5. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 1, characterized in that, In the geometric modeling of the ring cutter, the tool hysteresis angle varies with the axial height, specifically as follows: （5） In the formula, Let be the hysteresis angle of the k-th tooth as it changes with the tool axis.

6. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 3, characterized in that, In the geometric modeling of the ring cutter, the expression for calculating the tooth pitch angle is: （6） In the formula, Let be the tooth pitch angle between the k-th tooth and the (k-1)-th tooth as a function of axial height under the influence of tool runout. and These represent the actual cutting radii of the (k-1)th and kth teeth at the axial height z, respectively, affected by tool runout. Let z be the distance between the tips of the (k-1)th and kth teeth at the axial height z.

7. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 3, characterized in that, In the geometric modeling of the ring cutter, for a cutter with a constant helix angle, the tooth pitch angle remains constant, while for a cutter with a variable helix angle, the tooth pitch angle changes depending on the axial height, specifically as follows: （7） In the formula, Let be the tooth pitch angle between the k-th and (k-1)-th teeth of the cutting tool as a function of axial height. The pitch angle is the angle between the k-th tooth and the (k-1)-th tooth at the junction of the arc and cylindrical parts of the cutting tool.

8. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 3, characterized in that, In the geometric modeling of the ring cutter, under the influence of tool runout, the actual cutting radius expression is: （8） In the formula, This represents the tool runout offset. It varies with the axial height, specifically as follows: （9） In the formula, The runout position angle at the axial height R is [value missing]. Let be the tooth pitch angle at z for the k-th tooth and the reference tooth.

9. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 8, characterized in that, In the aforementioned micro-element contact modeling, during the cutting process, the radial depth of cut changes with the axial height, specifically as follows: （10） In the formula, The radial depth of cut varies with the tool axis. This is the nominal radial depth of cut.

10. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 8, characterized in that, In the aforementioned micro-element contact modeling, the expression for the feed per tooth under the influence of tool runout is: （11） In the formula, Let be the feed per tooth of the k-th tooth. is the average feed per tooth, and N is the number of cutting teeth.

11. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 8, characterized in that, In the aforementioned micro-element contact modeling, under the influence of tool runout, the expressions for the entry and exit angles during climb milling are: Angle of approach: （12） Cut-out angle: （13） In the formula, It is a multiple regeneration index. , The following relationship must be satisfied: （14） During conventional milling, the angle of entry is: （15） The cut-out angle is: （16）； The unit step function is used to determine whether the cutting teeth are cutting the workpiece; its expression is: （17）。 12. The method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 11, characterized in that, In the instantaneous undeformed cut thickness modeling, under the influence of multiple regeneration effects, the cut thickness expression is: （18） When tooth skipping occurs due to runout, the expression is: （19）。 13. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 12, characterized in that, In the dynamic cutting thickness modeling, the instantaneous undeformed cutting thickness includes both static and dynamic cutting thickness, expressed as: （20） In the formula, For static thickness cutting, For dynamic thickness cutting; The static cutting thickness expression under multiple regeneration effect is: （21） The dynamic cutting thickness expression under multiple regeneration effect is: （22） In the formula, , , These represent the vibrations of the tool in three directions during the current cutting tooth cycle. , , These represent the vibrations of the workpiece in three directions during the current cutter cycle. , , These represent the vibrations of the tool in three directions under the multiple regeneration effect. , , These represent the vibrations of the workpiece in three directions under the multiple regeneration effect.

14. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 13, characterized in that, The expression for the dynamic cutting force acting on the m-th axial cutting element of the k-th cutting edge of the tool at time t is: （23） In the formula, , , These are the cutting force coefficients in the tangential, radial, and axial directions, respectively; In the tool coordinate system, the infinitesimal cutting force is decomposed into forces along the x, y, and z directions, specifically: （24） The dynamic cutting force modeling, by summing all the infinitesimal cutting forces, yields the following expression for the total cutting force of the tool: （25） In the formula, This represents the discrete number of the cutting tool along the axial direction.

15. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 14, characterized in that, In the aforementioned mechanical identification method, without considering tool runout, the average cutting force per tooth is calculated as follows: （26） In the formula, , These represent the entry and exit angles, respectively. The cutting force was measured experimentally, and the specific expression was obtained by linear regression: （27） In the formula, , These are shearing force and cutting edge force, respectively.

16. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 15, characterized in that, In the aforementioned mechanical identification method, based on the obtained theoretical average cutting force and experimental measurements, the expression for the cutting force coefficient can be derived as follows: （28） （29） （30） （31） （32） （33） In the formula, , , The expression is: （34） （35） （36）。 17. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 14, characterized in that, The fluctuation parameter is achieved through an optimized identification method, which maps theoretical predictions to experimental measurements. The expression is as follows: （37） In the formula, , , These are the theoretical predictions for three directions, , , These are experimental measurements taken in three directions.

18. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to any one of claims 1-17, characterized in that, In the optimized identification method, the theoretical predicted value is divided into S parts within one revolution of the tool, as follows: （38） The theoretical cutting force expression is: （39）。 19. A method for modeling and identifying cutting force coefficients and runout parameters of a ring cutter according to claim 18, characterized in that, In the optimized identification method, the experimental measurement value under steady-state cutting conditions is expressed as: （40） In the formula, The sampling period is n, where n is a positive integer. Since the equation relating theoretical predictions and experimental measurements is a nonlinear overdetermined system of equations, it can be transformed into a nonlinear optimization problem, expressed as: （41） In the formula, Cutting force data selected at equal intervals from experimental measurements; In solving At that time, without any derivative information, the unconstrained nonlinear programming function Fminsearch is used to simultaneously identify the cutting force coefficient and runout parameter. During the identification process, the Nelder-Mead algorithm is used to continuously update the optimized value, so as to make the objective function more efficient under the condition of satisfying the iteration tolerance. Minimum.

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