Milling force modeling method for discrete edge end mill

Abstract

The invention belongs to the field of metal processing, and discloses a milling force modeling method for a discrete edge end mill. The method mainly comprises the steps that firstly, the discrete edge end mill is dispersed into cylindrical infinitesimal elements in the axial direction, whether chip dividing groove parts of the discrete edge end mill participate in cutting or not is judged, then milling force models of the chip dividing groove parts and non-chip dividing groove parts are established on the basis of an infinitesimal element method respectively, the non-chip dividing groove parts and the chip dividing groove parts are integrated in the axial direction of each circumferential edge, and the non-chip dividing groove parts and the chip dividing groove parts are integrated; and finally, summing the milling force acting on each circumferential blade unit to obtain the total milling force of the discrete blade end mill. The invention provides a milling force modeling method for a discrete edge end mill, which makes up for the milling force change condition caused by the fact that an existing milling force model cannot accurately describe the peripheral edge line discrete structure of the discrete edge end mill, and can better conform to the actual milling force change condition of the discrete edge end mill under the condition of obtaining the same prediction precision.

Description

Technical Field

[0001] The present invention belongs to the field of metal processing, and more specifically, relates to a method for modeling milling force of a discrete-edge end mill. Background Art

[0002] The application of discrete edge end mills in the machining of aerospace and deep cavity parts has solved some problems of traditional end mills, such as large tool overhang, high material removal rate leading to difficult chip removal, and tool chatter, thereby improving the surface machining quality of the workpiece and increasing machining efficiency. However, there is currently a key problem, that is, the lack of a milling force model that can accurately express the changes in the milling process of discrete edge end mills, resulting in the characteristics of the milling process of discrete edge end mills not being fully revealed.

[0003] Most of the existing milling force models are based on ordinary end mills. Although they have good general applicability, they lack consideration of the overall structure of discrete edge end mills, making it difficult to accurately predict the impact of discrete edge end mills on milling forces after structural changes compared to ordinary end mills. This limits the prediction of the stability of the milling process and the improvement of the surface quality accuracy of the workpiece. Summary of the invention

[0004] In order to retain the universality of the traditional milling force model and achieve a more accurate description of the milling force of discrete edge end mills, the present invention provides a discrete edge end mill milling force modeling method, which can guide the cutting process by predicting the changes in the milling force, so that the milling force is stable, and then the processing process is stable, which makes it easier to obtain better surface quality.

[0005] To achieve the above object, according to the present invention, a method for modeling milling force of a discrete edge end mill is provided, which is characterized by comprising the following steps:

[0006] (1) Establish the tool column coordinate system: the rightward feed direction of the discrete edge end mill is +x, the direction perpendicular to the workpiece surface is +y, the tool axis points to the spindle direction is +z, the tool rotation direction is clockwise and the rotation angle is θ, and the fan-shaped column microelement position is φ j ;

[0007] (2) Simplify the profile of the discrete edge end mill into a cylindrical shape, and divide the discrete edge end mill into cylinders with an angle of axial direction. The milling force received by any micro-edge in the cylinder in the cutting area is (dF t ,dF r ), the milling force on the micro-edge is shown in formula (1):

[0008]

[0009] Where, dF tj,1、dF rj,1 are the tangential force and radial force on the non-chip groove micro-edge, K tc , K rc are the tangential and radial milling force coefficients of the micro-element blade, dz is the axial length of the micro-element blade, g(φ j ) is a step function used to determine whether the cutter tooth j participates in cutting, h(φ j,1 ) is the instantaneous chip thickness of the non-chip groove part of the jth tooth. The instantaneous chip thickness h(φ j,1 ) is expressed as:

[0010] h(φ j,1 )=f z sinφ j,1 +(U j -U j,0 )

[0011] Where f z U is the feed per tooth of the flat-bottom spiral end mill; j -U j,0 It represents the dynamic displacement of the current tooth of the tool structure and the previous tooth cycle. Step function g(φ j ) and the radial contact angle φ at the axial height z of the non-chip groove part of the jth tooth at time t j,1 The definition of (t,z) is as follows:

[0012]

[0013]

[0014]

[0015] Where β is the helix angle of the discrete edge end mill; R is the radius of the edge line of the non-chip groove part of the discrete edge end mill; N represents the total number of teeth. θ = nt, n is the spindle speed, and t represents the time required to rotate through θ. e is the radial cutting depth; z is the axial height of the contact angle; φ st is the cutting angle of the discrete edge end mill; φ ex is the cutting angle of the discrete edge end mill; j represents the jth tooth of the discrete edge end mill.

[0016] (3) Through coordinate transformation, the milling force on the micro-element blade is converted into components in the rectangular coordinate system, which is expressed as follows:

[0017]

[0018] Where dF xj,1 、dF yj,1 They are respectively the micro-forces in x and y directions on the micro-edge of the non-chip groove part of the j-th tooth in the rectangular coordinate system.

[0019] (4) The resultant force on the discrete edge end mill in the rectangular coordinate system is:

[0020]

[0021] Where a p is the axial cutting depth; z ji represents the axial height of the i-th node of the j-th tooth; F xj,1 and F yj,1 are the milling forces of the cutting edge of the jth tooth in the non-chip groove part in the x and y directions, respectively.

[0022] (5) The main steps of establishing the milling force model of discrete edge end mills are as above. The milling force of the edge line of the discrete edge end mill has been established; the next step is to model the chip groove part of the discrete edge end mill. Similarly, there are:

[0023]

[0024] In the formula h(φ j,2 ) is the instantaneous chip thickness of the micro-edge of the j-th tooth chip groove. The instantaneous chip thickness h(φ j,2 ) and the radial contact angle φ at the axial height z of the chip groove at time t j,2 (t,z) is expressed as:

[0025]

[0026] h(φ j,2 )=f z sinφ j,2 +(U j -U j,0 )

[0027] Where R2 is the radius of the tool in the chip groove.

[0028] (6) It can be seen that the milling force at the chip groove can be expressed as:

[0029]

[0030] Where F xj,2 and F yj,2 are the milling forces of the cutting edges of the jth tooth in the chip groove part in the x and y directions, respectively.

[0031] (7) When the discrete edge end mill has a rotation angle of θ, the resultant milling force F in the x direction of the discrete edge end mill x and the milling force in the y direction F y They can be expressed as:

[0032]

[0033]

[0034] Where F xj and F yj are the resultant milling forces in the x and y directions of the j-th tooth, respectively.

[0035] Beneficial Effects of the Invention

[0036] The present invention can accurately calculate the milling force generated by the dynamic cutting process of the discrete edge end mill. Professional technicians can then predict the milling state of the discrete edge end mill based on the simulated dynamic changes of the milling force, thereby reasonably adjusting the processing parameters.

[0037] Instruction Manual

[0038] Figure 1 A geometric structure diagram of a discrete edge end mill of a discrete edge end mill milling force modeling method of the present invention;

[0039] Figure 2 A modeling flow chart of a method for modeling milling force of a discrete-edge end mill of the present invention;

[0040] Figure 3 It is an integral region diagram of a discrete edge end mill milling force modeling method of the present invention;

[0041] Figure 4 A milling force experiment scene diagram of a discrete-edge end mill milling force modeling method of the present invention;

[0042] Figure 5 This is a comparison diagram between experimental milling force and simulated milling force of a discrete edge end mill milling force modeling method of the present invention. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0044] Referring to the accompanying drawings, a method for modeling milling force of a discrete edge end mill comprises the following steps:

[0045] (1) Establish Figure 1 Tool column coordinate system: The right feed direction of the discrete edge end mill is +x, the direction perpendicular to the workpiece surface is +y, the tool axis points to the spindle direction is +z, the tool rotation direction is clockwise and the rotation angle is θ, and the fan-shaped column microelement position is φ j ;

[0046] (2) When the discrete edge end mill has a rotation angle of θ, the resultant force on the discrete edge end mill can be expressed as:

[0047]

[0048] The total cutting force in the x and y directions is composed of the cutting force of the non-chip groove part in the x and y directions and the cutting force of the chip groove part.

[0049] (3) Figure 3 The integral area of ​​the discrete edge end mill is shown. The discrete area on each cutting edge of the discrete edge end mill is different, so it is necessary to integrate each cutting edge of the discrete edge end mill separately. The milling force algorithm of a single cutting edge is as follows:

[0050]

[0051]

[0052]

[0053] The following will be combined with a specific example to more clearly explain the analytical optimization method of the present invention:

[0054] The geometric parameters of the discrete edge end mill used in this example are: milling cutter radius 16mm, helix angle 30 degrees, number of teeth 4. The discrete edge end mill material is cemented carbide, and the milling workpiece material is Al7075. Figure 4 This is a picture of the milling experiment site.

[0055] The milling method adopts down milling and side milling, and the radial cutting depth is a e =1mm, spindle speed n=2000r / min, feed per tooth is f z =0.05mm / r. The experiment was carried out on a VDL-1000E three-axis CNC milling machine. Table 1 shows the milling force coefficient K. tc , K rc Required parameter table; Figure 5 This is a comparison chart of the milling force image obtained experimentally and the milling force image simulated by software MATLAB2022b.

[0056] Table 1 Milling process parameters

[0057]

[0058] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for modeling milling force of discrete edge end mill, characterized in that: The following steps are involved: Step 1: Establish a discrete edge end mill coordinate system, establish the tangential and radial micro-element milling force formulas of the discrete edge end mill based on the micro-element method, and convert the tangential force and radial force into a rectangular coordinate system through coordinate transformation; Step 2: According to the different discrete intervals of the four peripheral edges of the discrete edge end mill, the milling force of each cutting edge is integrated separately to obtain the resultant force of the non-chip groove part of each cutting edge of the discrete edge end mill; Step 3, establishing a milling force model for the chip groove part by imitating the milling force model for the non-chip groove part of the discrete edge end mill in step 1 and step 2; Step 4: The milling force of each cutting edge includes the milling force generated by the chip groove part and the non-chip groove part. Finally, the milling forces generated by all the peripheral cutting edges of the discrete cutting edge end mill are superimposed in the x and y directions respectively to obtain the milling force model of the discrete cutting edge end mill.

2. The method for modeling milling force of a discrete edge end mill according to claim 1, characterized in that: Step 1 is as follows: (1) Establish the tool column coordinate system: the rightward feed direction of the discrete edge end mill is +x, the direction perpendicular to the workpiece surface is +y, the tool axis points to the spindle direction is +z, the tool rotation direction is clockwise and the rotation angle is θ, and the fan-shaped column microelement position is φ j ; (2) The profile of the discrete edge end mill is simplified to a cylindrical shape, and the discrete edge end mill is divided into cylinders with a thickness of dz along the axial direction. The milling force received by any micro-edge in the cylinder in the cutting area is (dF t ,dF r ), the milling force on the micro-edge is shown in formula (1): Where dF tj,1 、dF rj,1 are the tangential force and radial force on the non-chip groove part of the micro-edge, respectively. In this patent, subscript 1 represents the non-chip groove part, and subscript 2 represents the chip groove part; K tc , K rc are the tangential and radial milling force coefficients of the micro-element blade, dz is the axial length of the micro-element blade, g(φ j ) is a step function used to determine whether the cutter tooth j participates in cutting, h(φ j,1 ) is the dynamic chip thickness of the non-chip groove part of the jth tooth. The dynamic chip thickness h(φ j,1 ) is expressed as: h(φ j,1 )=f z sinφ j,1 +(U j -U j,0 ) Where f z U is the feed per tooth of discrete edge end mill; j -U j,0 It represents the dynamic displacement of the current tooth of the tool structure and the previous tooth cycle. The step function g(φ j ) and the radial contact angle φ of the non-chip groove portion of the jth tooth of the discrete edge end mill at the axial height z at time t j,1 The definition of (t,z) is as follows: Where β is the helix angle of the discrete edge end mill; R is the edge line radius of the non-chip groove part of the discrete edge end mill; N is the total number of teeth; θ = nt, n is the spindle speed, t is the time required to rotate θ; a e is the radial cutting depth; z is the axial height of the contact angle; φ st is the cutting angle of the discrete edge end mill; φ ex is the cutting angle of the discrete edge end mill; j represents the jth tooth of the discrete edge end mill; (3) Through coordinate transformation, the milling force on the micro-element blade is converted into components in the rectangular coordinate system, which is expressed as follows: Where dF xj,1 、dF yj,1 They are the micro-forces in x and y directions on the micro-edge of the non-chip groove part of the j-th tooth in the rectangular coordinate system.

3. The method for modeling milling force of a discrete edge end mill according to claim 1, characterized in that: Step 2 is as follows: The resultant milling force of the jth tooth of the discrete edge end mill in the non-chip groove area in the x and y directions is: Where a p is the axial cutting depth; z ji represents the axial height of the i-th node of the j-th tooth; F xj,1 and F yj,1 are the milling forces of the cutting edge of the jth tooth in the non-chip groove part in the x and y directions, respectively.

4. The method for modeling milling force of a discrete edge end mill according to claim 1, characterized in that: Step three is as follows: (1) Follow the steps of modeling the edge line of the discrete edge end mill, except that the radial contact angle and dynamic cutting thickness need to be changed: Where dF tj,2 、dF rj,2 are the tangential force and radial force on the non-chip groove part of the jth tooth, h(φ j,2 ) is the dynamic chip thickness of the micro-edge of the j-th tooth chip groove. The dynamic chip thickness h(φ j,2 ) and the radial contact angle φ at the axial height z of the j-th tooth chip groove at time t j,2 (t,z) is expressed as: h(φ j,2 )=f z sinφ j,2 +(U j -U j,0 ) Where R2 is the radius of the chip groove part of the discrete edge end mill; (2) It can be seen that the milling force at the chip groove can be expressed as: Where F xj,2 and F yj,2 are the milling forces of the cutting edges of the jth tooth in the chip groove part in the x and y directions, respectively.

5. The method for modeling milling force of discrete edge end mill according to claim 1, characterized in that: Step 4 is as follows: When the discrete edge end milling cutter has a rotation angle of θ, the resultant milling force F in the x direction of the discrete edge end milling cutter x and the milling force in the y direction F y They can be expressed as: Where F xj and F yj are the resultant milling forces in the x and y directions of the jth tooth, respectively.

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