A Method and System for Modeling the Side Milling Cutting Force of an Equal Gradient Helical Tool

Abstract

The present invention discloses a method and system for modeling the cutting force of an equal-variable pitch helical milling cutter, characterized in that the developed line of the variable pitch helical edge is a set function, a rectangular coordinate system fixed on the tool and a cutting edge micro-element coordinate system that rotates with the tool are established; an equation for the spatial edge line of the equal-variable pitch helical tool is established; by differentiating the helix angle of the cylindrical variable pitch helical milling cutter model, it is judged whether the micro-element participates in cutting; functions related to the helix angle such as different micro-element shear force coefficients and axial plowing force coefficients are obtained; the instantaneous cutting thickness and the helix angle value at the axial cutting depth of the tool are obtained; the predicted cutting forces in three directions during the side milling process of the equal-variable pitch helical tool are obtained. It solves the problem that the existing milling force model is not applicable to the prediction of the cutting force during the side milling process of the equal-variable pitch helical edge milling cutter, and can accurately predict the milling force during the side milling process of the equal-variable pitch helical milling cutter, so as to reasonably recommend the tool structure parameters, set the milling parameters and improve the machining accuracy.

Description

Technical Field

[0001] The present invention relates to the field of metal cutting, and particularly to the cutting technology of equal-variable-pitch helical milling cutters. Background Art

[0002] Milling as an advanced machining technology is widely used in the fields of aviation, aerospace, shipbuilding, mold, and automobile, etc. For the milling of thin-walled parts, the equal-variable-pitch helical-edge milling cutter can reduce the radial milling force, reduce the elastic deformation caused by the milling force during the cutting process, at the same time reduce the cutting vibration, improve the cutting stability, and further improve the dimensional accuracy and surface quality, and extend the tool life, thus having broad application prospects.

[0003] Cutting force is a very important physical quantity reflecting the information of the cutting process. Its magnitude and change have a direct impact on the machining stability, and at the same time have a certain impact on the machining surface quality, tool wear, and tool life. Reliable and quantitative cutting force prediction is of extremely important significance for both production practice and theoretical research. Therefore, accurately predicting the milling force of the equal-variable-pitch helical-edge cutter through a modeling method has a positive impact on optimizing the tool structure parameters, milling parameters, and improving the machining accuracy, thereby improving the milling efficiency and reducing the production cost, and having important economic value and practical significance.

[0004] The existing milling force model divides the milling cutter into finite cutting-edge micro-elements along the axis (Z-axis) of the milling cutter, obtains the micro-element lag angle according to the helix angle, calculates the tangential, radial, and axial force micro-elements of each micro-element, and judges the participation of the micro-elements in the cutting according to the engagement and disengagement angles, and then predicts the milling force by integrating along the axis and summing for each tooth. It is only applicable to the prediction of the milling force of a milling cutter with a single-edge-line helix angle that remains constant. The equal-variable-pitch helical edge means that the helix angle of this edge line is not a fixed value, but changes with the change of the axial dimension of the tool. The angular position of any point on the edge line is not only related to the rotation angle of the tool, but also related to the helix angle of the cutting point position. At the same time, each shear force and ploughing force milling force coefficient are functions related to the helix angle. In the calculation process of the existing milling force model, it is considered that the milling force coefficient is a constant and does not participate in the integration of the micro-element milling force. Therefore, the existing milling force model is not applicable to the prediction of the cutting force during the side milling process of the equal-variable-pitch helical-edge milling cutter. Summary of the Invention

[0005] The present invention provides a cutting force modeling method and system for an equal-variable-pitch helical milling cutter, which solves the problem that the existing milling force model is not applicable to the prediction of the cutting force during the side milling process of the equal-variable-pitch helical-edge milling cutter, and can accurately predict the milling force during the side milling process of the equal-variable-pitch helical milling cutter, so as to reasonably recommend the tool structure parameters, set the milling parameters, and improve the machining accuracy.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A method for modeling the side milling cutting force of an equal-gradient spiral cutter, characterized in that the developed line of the gradient spiral edge is a set function, and the method comprises the following steps:

[0008] S1: Establish a rectangular coordinate system fixed on the cutter and a cutting edge micro-element coordinate system that rotates with the cutter;

[0009] S2: Establish the spatial edge line equation of the equal-gradient spiral cutter;

[0010] S3: Obtain the parameters of the cylindrical gradient spiral milling cutter, including the number of teeth N, the diameter D, the rake angle of the cutter α0, the clearance angle of the cutter γ0, the helix angle β, and the radius of the tip edge circle r e , the axial cutting depth a p , the radial cutting depth a e ; where the helix angle β is a variable; by differentiating the helix angle, the milling cutter is divided into M cutting edge micro-elements, and the cutting depth micro-element or the micro-element axial length and the edge length micro-element or the micro-element cutting edge length in the cutter coordinate system are determined;

[0011] S4: By comparing the ranges of the milling cut-in angle and the cut-out angle and the cutting width, establish a window function to judge whether the micro-element u j participates in cutting;

[0012] S5: Collect the workpiece material parameters: the shear yield strength τ s , the shear angle φ0, the normal friction angle ζ0, and the chip flow angle η c . Combine the cutter parameters to obtain the tangential, radial, and axial shear force coefficients of different micro-elements, and the tangential, radial, and axial plowing force coefficients of different micro-elements;

[0013] S6: Collect the cutting parameters: the feed per tooth f N , the rotational speed n, and the cutting depth a p ; obtain the instantaneous cutting thickness and the helix angle value at the axial cutting depth a p of the cutter;

[0014] S7: Collect the workpiece material parameters: the shear yield strength, the shear angle, the normal friction angle, and the chip flow angle. Collect the cutter parameters: the number of cutter teeth, the cutter diameter, and the cutter helix angle, rake angle, clearance angle, tip edge circle radius, the edge length of the cutter, and the instantaneous position angle information; collect the cutting parameters: the feed per tooth, the rotational speed, and the cutting depth; obtain the milling force model of the equal-gradient spiral milling cutter indicated by the predicted cutting forces in the X, Y, and Z directions of the thin-walled part cut by the gradient spiral cutter.

[0015] In the above technical solution, the general form of the spatial edge line equation of the equal-gradient spiral cutter in step S2 is as follows:

[0016]

[0017] In Equation (1): β is the helix angle, satisfying β min ≤ β ≤ β max , rad; β min is the starting helix angle, rad; β max is the ending helix angle, rad; N is the number of teeth of the cutter; i is the number of cutting edges, a positive integer and satisfying 1 ≤ i ≤ N; D is the cutter diameter, mm; f is the functional relationship between the position angle and β, and z is the functional relationship between the Z coordinate and β.

[0018] In the above technical solution, the general model of the milling force of the variable pitch helical milling cutter in step S6 is as follows:

[0019]

[0020] In Equation (2), F x , F y , F z are the predicted cutting forces in the X, Y, and Z directions respectively during the side milling of thin-walled parts by the variable pitch helical cutter, N; β is the helix angle, satisfying β min ≤ β ≤ β max , rad; β min is the starting helix angle, rad; β max is the ending helix angle, rad; N is the number of teeth of the cutter; i is a positive integer and satisfying 1 ≤ i ≤ N; j is the microelement serial number; D is the cutter diameter, mm; l1 is the cutting edge length of the cutter, mm; φ ij is the instantaneous position angle, rad; g(φ ij ) is the window function; K tc , K rc , K ac are the tangential, radial, and axial shear force coefficients of the microelement u j ; K te , K re , K ae are the tangential, radial, and axial plowing force coefficients of the microelement u ij ; h D (φ ij ) is the instantaneous cutting thickness; β ap is the helix angle value at the axial cutting depth a p of the cutter.

[0021] In the above technical solution, the expression of the window function g(φ ij ) for judging whether the microelement u ij participates in cutting in step S4 is as follows:

[0022]

[0023] In Equation (3): φ stis the milling engagement angle, in rad; φ ex is the milling disengagement angle, in rad; and the two satisfy the relationship: 0 ≤ φ st <φ ex ≤ π;

[0024] In Equation (3), the engagement angle φ st , the disengagement angle φ ex are expressed as follows:

[0025]

[0026] In Equation (4), a e is the cutting width.

[0027] In the above technical solution, in step S5, the tangential, radial, and axial shear force coefficients K ij of the microelement u tc , K rc , K ac satisfy the following formula:

[0028]

[0029] In Equation (5), τ s is the shear yield strength, φ0 is the shear angle, α0 is the rake angle of the tool, ζ0 is the normal friction angle, η c is the chip flow angle.

[0030] In the above technical solution, in step S5, the tangential, radial, and axial plowing force coefficients K ij of the microelement u te , K re , K ae satisfy the following formula:

[0031]

[0032] In Equation (6), r e is the nose radius of the cutting edge, θ f is the splitting angle. Based on the splitting angle theory proposed by AbdelMoneim, θ f = ζ0;

[0033] In the above technical solution, in step S6, h D (φ ij ) is the instantaneous cutting thickness and is expressed as follows:

[0034]

[0035] In Equation (7), f is the feed rate, in mm / r; n is the rotational speed, in r / min; is the angular pitch between teeth, in rad;

[0036] In Equation (2), β ap is the helix angle value at the axial cutting depth a p of the tool, and satisfies the following formula:

[0037]

[0038] where D is the tool diameter, in mm.

[0039] In the above technical solution, the developed line of the variable pitch helix edge is one of a parabola, a hyperbola, or a logarithmic curve.

[0040] In the above technical solution, when the developed line of the variable pitch helix edge is a parabola, i.e., the quadratic function z(Dψ ij / 2) = a(Dψ ij / 2) 2 + b(Dψ ij / 2) + c, where a, b, and c are the coefficients of the quadratic function. Since the edge line passes through the origin of the developed coordinate system, c = 0; at this time, the coefficients a and b can be expressed by the helix angle β. After arrangement, the milling force model of the variable pitch end mill is as follows:

[0041]

[0042] An equal variable pitch helical tool side milling cutting force modeling system, characterized in that it is used to implement the above modeling method.

[0043] Compared with the prior art, the beneficial effects of the present invention are:

[0044] The dynamic cutting force model of a conventional cylindrical helical milling cutter is generally axially differentiated. During the calculation of the milling force model, it is considered that the milling force coefficient is a constant and does not participate in the integration of the differential cutting force. Therefore, the existing milling force model is not applicable to the cutting force prediction during the side milling process of an equal variable pitch helical edge milling cutter.

[0045] The cutting force model of a conventional cylindrical helical milling cutter calculates the differential force axially and then integrates to obtain the cutting force, which is not applicable to an equal variable pitch helical milling cutter. The present invention proposes to calculate the differential cutting force according to the helix angle differentiation, and on this basis, proposes a general milling force model for an equal variable pitch constant helix milling cutter. It can accurately predict the milling force during the side milling process of an equal variable pitch helical milling cutter.

[0046] Finally, the present invention also takes the developed line of the variable pitch helix edge as a quadratic function as an example, and accurately predicts the milling force of the quadratic function variable pitch helical tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0048] Figure 1It is a schematic flow chart of the cutting force modeling method for the variable pitch helical milling cutter of the present invention and the like.

[0049] Figure 2 It is a schematic diagram of the coordinate system of the variable pitch helical end mill of the present invention and the geometry of the cutting edge microelement.

[0050] Figure 3 It is a schematic diagram of the undeformed chip thickness of the instantaneous cutting microelement of the present invention.

[0051] Figure 4 Comparison diagram of the milling force model prediction and experimental results of the variable pitch helical edge cutter. Specific embodiments

[0052] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0053] In the cutting force modeling method and system for the variable pitch helical milling cutter implemented according to the present invention, the specific implementation is as follows:

[0054] The spatial equation M(x, y, z) of the variable pitch cylindrical helix is expressed as follows:

[0055]

[0056] In the formula, R is the radius of the cylinder where the variable pitch helix is located (tool radius), in mm; θ0 is the rotation position angle of the variable pitch helix, which is equal to the lag angle ψ j in the present invention, in rad; z(θ0R) is the functional relationship between the axial position z and θ0R. Different z functional relationships result in different degrees of variation of the cylindrical helix.

[0057] For the variable pitch gradient helical end mill, the starting angle and the ending angle of the helix angle of each cutting edge are the same, and the z function is the same, that is, each cutting edge is exactly the same, and the helix angle of each cutting edge gradually increases axially. Let N be the number of tool teeth (number of cutting edges), then the equation of the i-th (1 ≤ i ≤ N) cutting edge of the variable pitch helical end mill is as follows:

[0058]

[0059] In the process of calculating the milling force, the geometric shape of the cutting microelement is closely related to the contact form between the tool and the workpiece. Establishing an accurate tool geometric model is the basis for calculating the milling force. The milling process and the tool geometry are usually described by two sets of coordinate systems, namely the rectangular coordinate system fixed on the tool and the cutting edge microelement coordinate system that rotates with the tool, as Figure 1 shown.

[0060] (1) Tool rectangular coordinate system

[0061] For convenient observation, the tool is simplified to a cylinder, and the intersection point of the tool axis and the tool bottom surface is defined as the origin O of the tool rectangular coordinate system t , and the tool axis is defined as the Z t axis (positive upward vertically); the positive direction of the X t axis is the same as the feed direction, and the Y t axis is perpendicular to the workpiece surface (positive outward), and the tool coordinate system O t -X t Y t Z t is established.

[0062] (2) Micro-element coordinate system of the cutting edge

[0063] The solid end mill is discretized along the Z axis into M micro-element disks, and there are M cutting-edge micro-elements on each micro-element disk. Taking any micro-element cutting edge on any micro-element disk as an example, the center of the micro-element body is defined as the center o, the direction parallel to the tool axis is defined as the a axis (positive upward vertically), the direction pointing to the center of the disk is defined as the r axis (positive inward), and the tangent direction of the disk is defined as the t axis (the positive direction is determined by the right-hand screw rule), and the micro-element coordinate system o-tra is established. Then the micro-element coordinate system on the i-th cutting edge is o i -t i r i a i .

[0064] As Figure 1 shown, let the diameter of a certain cylindrical equal-variable helix end mill be D (radius R), the number of tool teeth / edges be N, the helix angle of the tool side edge be β and β min ≤β≤β max , the helix angle is a variable, the tooth space angle of the tool is φ, the axial cutting depth is a p , and the radial cutting depth (cutting width) is a e . The position angle at the tip of the i-th cutting edge is φ i . Due to the existence of the helix angle, there is a lag during the milling process. Let the axial micro-element at the j-th (1≤j≤M) position on the i-th cutting edge be dz, and the lag angle of this micro-element be ψ j , and the position angle is φ j .

[0065] Let f be the functional relationship between the rotation position angle θ0 of the variable helix of the i-th cutting edge and the helix angle β:

[0066] θ0 = f(β) (3)

[0067] Suppose that at time t, the line connecting the tip of a certain cutting edge of the milling cutter and the origin of the workpiece coordinate system and the Y of the tool rectangular coordinate system tThe included angle in the positive direction of the axis (the included angle between the reverse direction of the infinitesimal r-axis and the positive direction of the tool Y t axis) is θ, then θ is called the radial position angle (initial position angle) of the first cutting edge, and can be expressed as follows:

[0068]

[0069] In the formula, n is the rotational speed of the milling cutter during milling, r / min; t is the time, s;

[0070] From Figure 1 it can be seen that the radial position angle φ at the tip of the i-th cutting edge can be expressed as follows:

[0071]

[0072] Since the helix angle is variable, there is a one-to-one correspondence functional relationship between the lag angle and the helix angle. Assume that the lag angle ψ ij of the cutting infinitesimal u j has the following relationship:

[0073] ψ ij = u(β) (6)

[0074] In the formula, u is the functional relationship between the lag angle ψ j of the i-th cutting edge and the helix angle β.

[0075] Therefore, the magnitude of the radial position angle φ ij of the infinitesimal u j can be expressed as:

[0076]

[0077] According to the mechanical type II mechanical model proposed by ALTINTAS, it can be known that the three-direction milling forces on the infinitesimal u j can be expressed by the following formula:

[0078]

[0079] In the formula: dF t , dF r , dF a are the tangential, radial and axial milling forces on the infinitesimal u j respectively, N; K tc , K rc , K ac are the tangential, radial and axial shear force coefficients of the infinitesimal u ij respectively; K te , K re , K ae are the tangential, radial and axial plowing force coefficients of the infinitesimal u j respectively; dz, ds are the infinitesimal uij The depth-of-cut element and the edge-length element of it; φ(β,t) is the radial position angle of element u ij at time t, in rad; h D (φ(β,t)) is the cutting thickness of element u ij at time t, in mm; g(φ ij ) is the window function for judging whether there is cutting;

[0080] Element u j 's tangential, radial and axial shear force coefficients K tc , K rc , K ac satisfy the following formula:

[0081]

[0082] In the formula, τ s is the shear yield strength, φ0 is the shear angle, α0 is the tool rake angle, ζ0 is the normal friction angle, η c is the chip flow angle.

[0083] It can be seen from the formula that since the helix angle is a variable in the milling force model coefficient of the equal-variable-pitch helical-edge milling cutter, each coefficient is not a fixed value and changes with the change of the helix angle. Therefore, the calculation process of the milling force element is different from that of the traditional milling force model.

[0084] Element u ij 's tangential, radial and axial ploughing force coefficients K te , K re , K ae satisfy the following formula:

[0085]

[0086] In the formula, r e is the nose-edge radius, θ f is the splitting angle. Based on the splitting angle theory proposed by AbdelMoneim, θ f =ζ0.

[0087] When the diameter of the tool is much larger than the feed per tooth, the cutting edge trajectory of the milling cutter is approximately circular, and the undeformed cutting thickness can be simplified to solve. The geometric characteristics of the cutting contact area between the tool and the workpiece during the cutting process change with time. The accuracy of the instantaneous chip thickness model will directly affect the calculation accuracy of the cutting force model. In the two-dimensional theoretical analysis of side milling, the shape of the cutting area is fan-shaped, as Figure 2 shown.

[0088] Let the feed per tooth of the i-th cutting edge be f N , then there is

[0089]

[0090] In the formula, f is the feed per revolution, in mm / r;

[0091] When the cutting edge of the tool microelement participates in cutting, the instantaneous feed displacement can be ignored, and it can be considered that the tool tip starts to contact the surface to be machined of the workpiece at point A j until it leaves the machined surface of the workpiece at point B j and experiences a curve on the workpiece surface as shown in Figure A j B j Therefore, the length of the undeformed cutting thickness h ij of the jth cutting microelement u Dj on the ith cutting edge can be expressed as:

[0092] h D (φ ij ) = f N sin(φ ij ) (12)

[0093]

[0094] Since only when the cutting edge contacts the workpiece during side milling will cutting occur, a window function g(φ ij ) is needed to determine whether the microelement u j participates in cutting, and its expression is as follows:

[0095]

[0096] In the formula: φ st is the cutting-in angle of milling, in rad; φ ex is the cutting-out angle of milling, in rad; and the two satisfy the relationship: 0 ≤ φ st <φ ex ≤ π;

[0097] It can be seen that the key to solving the cutting force microelement model is to determine the instantaneous cutting thickness model and the magnitudes of the cutting-in and cutting-out angles. The cutting-in angle φ st and the cutting-out angle φ ex can be expressed as follows:

[0098]

[0099] The depth-of-cut microelement (axial length of the microelement) dz and the cutting-edge length microelement (cutting-edge length of the microelement) ds in the tool coordinate system, combined with Equation 2-1, can be used to obtain the axial length dz of the microelement in the tool coordinate system:

[0100]

[0101] Then the length ds of the microelement cutting edge can be expressed as:

[0102]

[0103] Through coordinate transformation, it is transformed into the tool coordinate system as follows:

[0104]

[0105] After sorting, the cutting force components acting in the rectangular coordinate system can be obtained as follows:

[0106]

[0107] The milling force distributions along the tangential, radial, and axial directions on the effective cutting edge of the tool at any time t are as Figure 3 shown. By integrating along the axial β angle and summing for each tooth, the instantaneous cutting forces acting on the entire milling cutter in the feed, normal, and axial directions can be obtained as follows:

[0108]

[0109] where β ap is the helix angle value at the axial position a p of the tool, and satisfies the following formula:

[0110]

[0111] In this invention, taking each edge line of the tool as the simplest uniform variable helix angle as an example, that is, each cutting edge of the tool increases according to the form of a quadratic function, and based on this, a dynamic cutting force model for side milling of an equal variable helix milling cutter based on a quadratic function is deduced to verify the accuracy of the milling force model. The quadratic function is as follows:

[0112] z(Dψ ij / 2) = a(Dψ ij / 2) 2 + b(Dψ ij / 2) + c (22)

[0113] In the formula, a, b, and c are the coefficients of the quadratic function. Since the edge line passes through the origin of the unfolded coordinate system, c = 0.

[0114]

[0115] Combining Equation (22) and Equation (23), the lag angle formula is as follows:

[0116]

[0117] After sorting, the position angle at time t:

[0118]

[0119] Combined with Equation (15), the infinitesimal axial length \(dz\) in the tool coordinate system is as follows:

[0120]

[0121] Combined with Equation (17), the length \(ds\) of the infinitesimal cutting edge can be expressed as:

[0122]

[0123] Substituting the above results into Equation (20), the milling force model of the variable pitch helical end mill based on the quadratic function is as follows:

[0124]

[0125] Among them, as can be seen from Equation (21), \(\beta\) ap satisfies:

[0126]

[0127] In summary, the instantaneous milling force during the cutting process of the equal variable pitch helical edge milling cutter can be obtained by using the above formula.

[0128] The correctness of the milling force model is verified through MATLAB simulation and experimental research.

[0129] The workpiece and tool parameters are as follows: The workpiece material is titanium alloy TC4, the workpiece thickness is 5 mm, the tool diameter \(D = 12\) mm, the number of tool teeth / flutes is \(N = 5\), the tool edge length \(l1 = 30\) mm, the helix angle of the tool side edge is \(\beta = 40^{\circ}-45^{\circ}\), and the tooth space angle of the tool is

[0130] The experimental machine tool is the Weili gantry machining center RB212 in Taiwan, China. The hardware part of the milling force signal acquisition system consists of a force sensor, a charge amplifier, and a data acquisition card. The KISTLER 9139A three-axis piezoelectric dynamometer and DH5922 data acquisition box are used to collect the milling force signals in the X, Y, and Z directions. The software of the milling force signal acquisition system uses the DynoWare3.2.2.0 - 1.0 software provided by Kistler Instruments AG in Switzerland, and the force signal acquisition frequency is set to 10 kHz. The spindle speed \(n = 3500\) r / min, the feed per tooth \(f\) N \(= 0.02\) mm / min, the axial cutting depth is \(a\) p \(= 17\) mm, the radial cutting depth (cutting width) is \(a\) e \(= 0.1\) mm, and the milling method is up milling dry cutting. The predicted and experimental results of the instantaneous cutting forces in the three directions of \(Fx\), \(Fy\), and \(Fz\) when the tool rotates one week (\(360^{\circ}\)) are as Figure 4 shown.

[0131] It should be understood that those of ordinary skill in the art can make improvements or modifications based on the above description, and all such improvements and modifications shall fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for modeling cutting force of side milling with a uniformly variable spiral tool, characterized in that The gradual spiral blade development line is a setting function, which includes the following steps: S1: Establish a rectangular coordinate system fixed on the tool and a cutting edge micro-element coordinate system that rotates with the tool; S2: Establish the spatial edge line equation of the uniformly variable spiral tool; S3: Get the tool parameters of the cylindrical gradual spiral milling cutter, including the number of tool teeth N, tool diameter D, mm, blade length l1, rake angle α0, back angle γ0, and tool tip radius r e , axial cutting depth a p , radial cutting depth a e , helix starting angle β min With the helix termination angle β max , satisfying β min ≤β≤β max , where the helix angle β is a variable, rad; by differentiating the helix angle, the milling cutter is divided into M cutting edge micro-elements u ij , determine the differential element u ij The micro-element axial length dz and the micro-element cutting edge length ds in the tool coordinate system; S4: By comparing the milling entry angle and the cutting angle range and the cutting width, a window function is established to determine the microelement u ij Whether to participate in cutting; S5: Collect workpiece material parameters: shear yield strength τ s , shear angle φ0, normal friction angle ζ0, chip flow angle η c ; Combined with the tool parameters, different micro-element shear force coefficients in the tangential, radial and axial directions, as well as different micro-element ploughing force coefficients in the tangential, radial and axial directions are obtained; S6: Collect cutting parameters: feed per tooth f N , speed n, cutting depth a p ; Obtain instantaneous cutting thickness and tool axial cutting depth a p The helix angle value at ; S7: Using the workpiece material parameters and the blade length and instantaneous position angle information of the tool; collecting cutting parameters: feed per tooth, rotation speed, cutting depth; obtaining the milling force model of the equal-gradient spiral milling tool indicated by the predicted cutting force in the three directions of X, Y, and Z when the gradient spiral tool cuts the thin-walled workpiece as follows: In the formula, F x 、F y 、F z are the predicted cutting forces in the X, Y and Z directions during the side milling of thin-walled parts by a gradual spiral tool, in N; i is the number of blade lines, a positive integer satisfying 1≤i≤N; j is the microelement number; φ ij is the instantaneous position angle, rad; f is the functional relationship between the position angle and β, z is the functional relationship between the Z coordinate and β; g(φ ij ) is the window function for determining whether to cut; K tc , K rc , K ac is the infinitesimal element u ij The tangential, radial and axial shear force coefficients; K te , K re , K ae is the infinitesimal element u ij Tangential, radial and axial plowing force coefficients; h D (φ ij ) is the instantaneous cutting thickness; β ap Axial cutting depth of the tool a p The helix angle value at .

2. The method for modeling cutting force of side milling with a uniformly variable spiral tool according to claim 1 is characterized in that Step S2 The spatial edge line equation of the gradient spiral tool is as follows: Where: β is the helix angle, satisfying β min ≤β≤β max , rad; β min is the starting angle of the spiral, rad; β max is the spiral termination angle, rad; N is the number of tool teeth; i is the number of blade lines, a positive integer that satisfies 1≤i≤N; D is the tool diameter, mm; f is the functional relationship between the position angle and β, and z is the functional relationship between the Z coordinate and β.

3. The method for modeling cutting force of side milling with a uniformly variable spiral tool according to claim 1 is characterized in that Step S4 determines the microelement u ij Whether to participate in the cutting window function g(φ ij ) is expressed as follows: Where: φ st is the milling cutting angle, rad; φ ex is the milling cut-out angle, rad; and the two satisfy the relationship: 0≤φ st <φ ex ≤π; Where the cutting angle φ st , cut-out angle φ ex It is expressed as follows: a e is the cutting width.

4. The method for modeling cutting force of side milling with a uniformly variable spiral tool according to claim 1, characterized in that In step S5, the infinitesimal element u ij The tangential, radial and axial shear force coefficients K tc , K rc , K ac Satisfies the following formula: In the formula, τ s is the shear yield strength, φ0 is the shear angle, α0 is the tool rake angle, ζ0 is the normal friction angle, η c is the chip flow angle; Microelement ij The tangential, radial and axial plowing force coefficients K te , K re , K ae Satisfies the following formula: In the formula, r e is the radius of the cutting edge, θ f is the shunt angle. Based on the shunt angle theory proposed by AbdelMoneim, θ f =ζ0.

5. The method for modeling cutting force of side milling with a uniformly variable spiral tool according to claim 1, characterized in that In step S6, D (φ ij ) is the instantaneous cutting thickness expression as follows: In the formula, f N is the feed per tooth, mm / r / N; n is the rotation speed, r / min; is the inter-tooth angle, rad; t is any time when the tool is cutting, in seconds; In the formula, β ap Axial cutting depth of the tool a p The helix angle value at satisfies the following formula: Where D is the tool diameter, mm.

6. The method for modeling cutting force of side milling with a uniformly variable spiral tool according to claim 1, characterized in that The gradual spiral blade development line is a parabola, a hyperbola or a logarithmic curve.

7. The method for modeling cutting force of side milling with a uniformly variable spiral tool according to claim 1, characterized in that The workpiece is a thin-walled part.

8. The method for modeling cutting force of side milling with a uniformly variable spiral tool according to claim 1, characterized in that The expansion line of the gradual spiral blade is a parabola, that is, a quadratic function z(Dψ ij / 2)=a(Dψ ij / 2) 2 +b(Dψ ij / 2)+c, where D is the tool diameter, mm; ψ ij is the lag angle, a, b and c are the coefficients of the quadratic function, where c = 0 because the edge line passes through the origin of the unfolded coordinate system; the coefficients a and b are expressed by the helix angle β, and the milling force model of the gradual helical end mill is as follows: l1 is the blade length of the tool, mm; g(φ ij ) is the window function for determining whether to cut; K tc , K rc , K ac is the infinitesimal element u ij The tangential, radial and axial shear force coefficients; K te , K re , K ae is the infinitesimal element u ij Tangential, radial and axial plowing force coefficients; h D (φ ij ) is the instantaneous cutting thickness; β ap Axial cutting depth of the tool a p The helix angle value at .

9. A cutting force modeling system for side milling of a uniformly variable spiral tool, characterized in that Used to implement the cutting force modeling method for side milling of a uniformly variable spiral tool as described in any one of claims 1 to 8.

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