CN-116360344-B - Method for analyzing machining stability in five-axis numerical control small radial deep cutting of ball end mill

Abstract

The invention belongs to the field of machine manufacturing, and provides a method for analyzing processing stability in five-axis numerical control small radial cutting depth of a ball-end milling cutter, which establishes a five-axis numerical control processing dynamics model of the ball-end milling cutter considering runout, develops a high-efficiency construction model of a cutter-workpiece contact area boundary under the influence of the runout, the CWE separation technology for accurately and efficiently determining the time lag period corresponding to each cutting infinitesimal is developed, the high-efficiency and high-precision prediction of the processing stability of the ball end mill under the five-axis numerical control small radial cutting depth is realized, and the method has great significance in realizing high-performance numerical control milling.

Inventors

• DAI YUEBANG
• LI HONGKUN
• LIU XUEJUN
• OU JIAYU
• CAO SHUNXIN
• BAO CUIMIN
• YANG SHUHUA
• LIU HAIBO
• YONG JIANHUA

Assignees

• 大连理工大学
• 沈阳透平机械股份有限公司

Dates

Publication Date

20260512

Application Date

20230316

Claims (3)

1. 1. A method for analyzing the processing stability in five-axis numerical control small radial deep cutting of a ball end mill is characterized by comprising the following steps: step 1.1, five-axis numerical control machining dynamics modeling Step 1.1.1) establishing a ball end mill motion trail mathematical model Establishing three coordinate systems, wherein the first coordinate system is a feeding coordinate system O-X f Y f Z f , the second coordinate system is a main shaft coordinate system O-X s Y s Z s , the third coordinate system is a workpiece coordinate system O w -X w Y w Z w , the point O is the sphere center of a ball end milling cutter of a path planning, in the feeding coordinate system O-X f Y f Z f , an axis Z f is perpendicular to the workpiece processing surface, an axis X f coincides with the feeding direction of the path planning, the main shaft coordinate system O-X s Y s Z s is obtained by rotating an axis X f and an axis Y f of the feeding coordinate system O-X f Y f Z f according to the cutter front inclination angle and the cutter side inclination angle, the workpiece coordinate system O w -X w Y w Z w is obtained from the point O to the point O w by translating the feeding coordinate system O-X f Y f Z f , the cutter coordinate system O-X t Y t Z t is established, the cutter coordinate system O-X t Y t Z t coincides with the main shaft coordinate system O-X s Y s Z s , and the axis Z t coincides with the cutter axis of the path planning; the ith cutting micro element on the jth cutter tooth of the ball end milling cutter is named as P, the corresponding axial angle is k, and the point P is defined as follows in a cutter coordinate system O-X t Y t Z t : (1) Wherein, the (2) Wherein R represents the radius of the milling cutter, mu represents the helical angle of the cutter teeth, t is the rotation time of the main shaft of the machine tool, k is the axial angle, the variation range is [0, pi/2 ], As the rotation angle of the main shaft of the machine tool, phi ji is the radial lag angle, N f is the number of cutter teeth for cutting the micro-element rotation angle; step 1.1.2) milling dynamics modeling with jitter considered The relationship of the feed coordinate system O-X f Y f Z f and the tool coordinate system O-X t Y t Z t is defined as follows: (3) Wherein [ X f , y f , z f ] T and [ X t , y t , z t ] T ] are the coordinates of points within the feed coordinate system O-X f Y f Z f and the tool coordinate system O-X t Y t Z t , respectively, T t and T l are defined in formula (4), wherein α and β are the tool rake angle and the roll angle, respectively; , (4) Tangential cutting force dF acting on point P t Radial cutting force dF r And axial cutting force dF a Represented as (5) Wherein K tc 、K rc and K ac are respectively a tangential cutting force coefficient, a radial cutting force coefficient and an axial shearing force coefficient, db is a cutting width, db= Rdk; The dynamic displacement of the P point in the feed coordinate system O-X f Y f Z f is expressed as X (T) -X (T-T (j, k)), y (T) -y (T-T (j, k)) and z (T) -z (T-T (j, k)), wherein T (j, k) is the time lag period corresponding to the P point, abbreviated as T j,k , and the instantaneous undeformed cutting thickness h (j, k, T) corresponding to the P point is expressed as (6) Wherein, for a cutter with equidistant cutter teeth, T j, k = g (j, k) T, wherein, T is a basic time lag period, the size is equal to 60/omega/N f , omega is the rotation speed of a main shaft of a machine tool, N f is the number of the cutter teeth, g (j, k) belongs to {1, 2, N f }, represents that the point P is cutting the material left by the g (j, k) th front cutter tooth, g (j, k) is simplified to g j, k , and V is defined as (7) In the tool coordinate system O-X t Y t Z t , the cutting force acting on point P is expressed as (8) Wherein T m is defined as Dynamic cutting force acting on ball end mill is obtained in workpiece coordinate system O w -X w Y w Z w by conversion between tool coordinate system and workpiece coordinate system Is that (9) Wherein k max , j and k min , j are respectively the maximum axial angle and the minimum axial angle of the j-th cutter tooth participating in cutting at the moment t; In the object coordinate system O w -X w Y w Z w , Represented as (10) The process (10) is simplified into (11) Wherein the method comprises the steps of , (12) Based on equation (12), the kinetic equation taking into account the runout is established as (13) Wherein M, C and K are respectively the modal mass, damping and rigidity of the processing system; Step 1.2, tool-workpiece contact area analytical model considering runout The tool-workpiece contact area model CWE mainly comprises an a line, a b line, a c line and a d line, a tool coordinate system O-X t Y t Z t and a spindle coordinate system O-X s Y s Z s are superposed together, a ball head part of the ball head milling cutter is monotonically distributed along the cutter shaft direction, the three-dimensional CWE model is replaced by a projection of the ball head part of the ball head milling cutter in a plane perpendicular to the cutter shaft line, namely a coordinate system O-X t Y t , the three-dimensional modeling is converted into two-dimensional modeling, wherein the coordinate system O-X t Y t is a two-dimensional coordinate system when the tool coordinate system O-X t Y t Z t is Z t =0, the relation shown in the formula (3) illustrates that the projection of the CWE in the tool coordinate system O-X t Y t Z t and the projection of the tool coordinate system O-X f Y f Z f are mutually mapped, when a projection equation of the CWE in the O-X f Y f is constructed, a projection equation of the CWE in the coordinate system O-X t Y t can be constructed according to the formula (3), wherein the coordinate system O-X f Y f is a projection equation of the CWE in the two-dimensional coordinate system O-X494 when the feed coordinate system O-X f Y f Z f is Z f =0, and the relation shown in the following projection equation of the coordinate system is constructed in the projection equation of the coordinate system of the CWE in the feed coordinate system O-X t Y t : 1.2.1 A) line a The point of line a is defined as (X t , y t , z t ) in the tool coordinate system O-X t Y t Z t , and the projection equation of line a in the coordinate system O-X t Y t is Wherein w is the depth of cut; 1.2.2 Line b and line d) The projection equation of the line b and the line d in the coordinate system O-X t Y t is determined by transient cutting force signals obtained by testing; 1.2.3 Line c) The projection equation of the line C in the coordinate system O-X t Y t is obtained by connecting the point B and the point C, wherein the point B and the point C are respectively the first points of the projection of the line B and the line d when seen from the negative direction of the Y t axis to the positive direction of the Y t axis in the coordinate system O-X t Y t ; Step 1.3, determining a time lag period corresponding to a cutting infinitesimal and a limit axial angle of a cutter tooth participating in cutting Determining a time lag period corresponding to the cutting primordia, identifying a maximum axial angle and a minimum axial angle of each cutter tooth participating in cutting, and establishing a kinetic equation considering jumping, wherein the time lag period corresponding to the cutting primordia and a limit axial angle of the cutter tooth participating in cutting are determined as follows; All cutting edges are projected on a coordinate system O-X t Y t , the cutting edges rotate around an O point, and for the ith cutting element of the jth cutter tooth, whether the cutting element falls into a CWE model established by the corresponding cutter tooth or not is judged at each moment; Judging whether the cutting element falls into a coupling area of a CWE model constructed by the first cutter tooth and the second cutter tooth when the cutting element is participating in cutting, and recording an axial angle corresponding to the cutting element when the cutting element falls into the coupling area, wherein the coefficient g j,k =1; By the method, whether each cutting element of the jth cutter tooth participates in cutting or not is determined, and the coefficient g j,k and the axial angle corresponding to the cutting element participating in cutting are determined; Determining a time-lag period corresponding to the ith cutting element of the jth cutter tooth through a formula T j, k = g j,k T, wherein the T is a basic time-lag period, the size of the T is equal to 60/omega/N f , omega is the rotating speed of a main shaft of a machine tool, and N f is the number of cutter teeth; When the coefficient g j,k =1, determining the maximum value and the minimum value of the axial angle recorded when g j,k =1, wherein the maximum value of the axial angle is the maximum axial angle k max , j when the j-th cutter tooth time lag period g j,k T, and the minimum value of the axial angle is the minimum axial angle k min , j when the j-th cutter tooth time lag period g j,k T; When the coefficient g j,k =2, determining the maximum value and the minimum value of the axial angle recorded when g j,k =2, wherein the maximum value of the axial angle is the maximum axial angle k max , j when the j-th cutter tooth time lag period g j,k T, and the minimum value of the axial angle is the minimum axial angle k min , j when the j-th cutter tooth time lag period g j,k T; Step 1.4, construction method of processing stability lobe diagram Discretizing the spindle rotating speed and cutting depth range, constructing a state transition matrix phi corresponding to each spindle rotating speed and cutting depth combination, determining a processing state corresponding to the milling process parameter by comparing the relation between the maximum value of a characteristic value mode of the state transition matrix phi and 1, constructing a processing stability lobe diagram, and realizing the optimization of the milling process parameter without chatter.
2. 2. The method for analyzing the processing stability in the five-axis numerical control small radial cutting depth of the ball end mill according to claim 1, wherein the method for determining the projection equation of the b-line and the d-line in the step 1.2 is specifically as follows: 2.1 Line b) The intersection point of the a line and the b line is named as a point A, and the specific process of obtaining the projection equation of the b line in the coordinate system O-X t Y t is as follows: 2.1.1 Determining the cutter rotation angle corresponding to the point A according to the transient cutting force signal obtained by the test; 2.1.2 The cutting edge is projected on a coordinate system O-X t Y t , the rotation angle of the cutting edge is changed based on the angle determined in 2.1.1), and the intersection point of the line a and the cutting edge in the coordinate system O-X t Y t is determined, wherein the intersection point is the projection of the point A in the coordinate system O-X t Y t ; 2.1.3 Converting the intersection determined in 2.1.2) to a feed coordinate system O-X f Y f Z f by a relation shown in formula (3), and determining a space straight line OA equation in the feed coordinate system O-X f Y f Z f ; 2.1.4 Converting the space linear OA equation from the feed coordinate system O-X f Y f Z f to the tool coordinate system O-X t Y t Z t by the formula (3) to obtain a projection equation of the b line in the coordinate system O-X t Y t ; 2.1.5 2.1.1) -2.1.4), determining projection equations of lines b corresponding to other cutting edges; 2.2 D number line The intersection point of the line a and the line D is named as the point D, under the condition of no jump, the line D is related to the cutter radius R, the cutting depth w and the cutting line spacing a l under the condition of no jump, under the condition of jump, the cutting line spacing is changed by the jump, and the projection equation of the line D in the coordinate system O-X t Y t is solved as follows: 2.2.1 Determining the cutter rotation angle corresponding to the point D according to the transient cutting force signal obtained by the test; 2.2.2 Based on the angle determined by 2.2.1), changing the rotation angle of the cutting edge to determine an intersection point of the line a and the cutting edge in the coordinate system O-X t Y t , wherein the intersection point is the projection of the point D in the coordinate system O-X t Y t ; 2.2.3 From the relation shown in formula (3), converting the intersection point determined in 2.2.2) into a feed coordinate system O-X f Y f Z f , the projection coordinates of the intersection point in the coordinate system O-X f Y f being defined as The cutting line spacing is destroyed by radial runout, and the cutting line spacing is regarded as L=a l - + The combination of the line a and the line e can determine the projection coordinate of the point D on the coordinate system O-X f y f , the line e is a processing trace left by the last tool path on the processing surface of the workpiece, the projection coordinate of the point D in the coordinate system O-X f y f is shown as a formula (14), wherein X is the coordinate value of the point D on the axis X f corresponding to the coordinate system O-X f Y f , and Y is the coordinate value of the point D on the axis Y f corresponding to the coordinate system O-X f Y f ; (14) 2.2.4 Converting the d-line equation from the feed coordinate system O-X f Y f Z f to the tool coordinate system O-X t Y t Z t by the formula (3) to obtain a projection equation of the d-line in the coordinate system O-X t Y t ; 2.2.5 2.2.1) -2.2.4), the d-line projection equation corresponding to other cutting edges is determined.
3. 3. The method for analyzing the processing stability in the five-axis numerical control small radial depth of cut of the ball end mill according to claim 1, wherein in the step 1.3), the number of cutter teeth N f =2.

Description

Method for analyzing machining stability in five-axis numerical control small radial deep cutting of ball end mill Technical Field The invention belongs to the field of machine manufacturing, and relates to metal milling, in particular to a method for analyzing processing stability in five-axis numerical control small radial deep cutting of a ball end mill. Background As a typical high-flexibility machining mode, the five-axis numerical control machining of the ball-end milling cutter is widely applied to the machining of key parts of aero-engines, compressors and other equipment, and the five-axis numerical control flutter-free machining of the ball-end milling cutter is significant. By describing the dynamic characteristics of the processing system by using a time-lag differential equation, a critical stability curve, namely a processing stability lobe diagram (stability lobe diagram is abbreviated as SLD) can be drawn, the main shaft rotating speed and cutting depth plane is divided into a stable area and an unstable area, and chatter caused by self-excited vibration can be effectively avoided by selecting parameters below the critical stability curve. Therefore, how to efficiently and accurately develop the five-axis numerical control machining dynamics analysis of the ball end mill, and accurately construct a machining stability lobe diagram are significant. Many scholars at home and abroad have proposed a lot of five-axis numerical control processing stability analysis methods of ball end mill, but these methods are mainly aimed at ideal processing state, in the course of small radial cutting depth, the jump especially radial jump has great influence on the processing process, it directly causes cutting state between cutter teeth to be disturbed, the cutter is deformed with work piece contact area, serious jump even causes partial cutter teeth not to cut, the cutting system is also converted into the multiple time-lag system from the ideal system of single time lag, therefore, how to develop the processing stability analysis method considering cutter jump is the key problem to be solved urgently. According to the invention, a machining dynamics modeling and stability analysis method research is carried out aiming at five-axis numerical control small radial cutting depth of the ball-end milling cutter, a five-axis numerical control machining dynamics model of the ball-end milling cutter considering radial runout is established, a ball-end milling cutter-workpiece contact area (BWE) boundary efficient construction model under the influence of radial runout is developed, a technology for accurately and efficiently identifying a time lag period corresponding to each cutting element and a cutting tooth participating in a cutting limit axial angle is developed, and the efficient and high-precision prediction of machining stability under the five-axis numerical control small radial cutting depth of the ball-end milling cutter is realized. Disclosure of Invention According to the invention, a machining dynamics modeling and stability analysis method research is carried out aiming at five-axis numerical control small radial cutting depth of the ball-end milling cutter, a five-axis numerical control machining dynamics model of the ball-end milling cutter considering jumping is established, a ball-end milling cutter-workpiece contact area (BWE) efficient construction model under the influence of jumping is developed, a technology for accurately and efficiently identifying the time lag period corresponding to each cutting element and the axial angle of the cutter tooth participated in the cutting limit is developed, and the efficient and high-precision prediction of the machining stability of the ball-end milling cutter under the five-axis numerical control small radial cutting depth is realized. The method comprises the following steps: 1. five-axis numerical control machining dynamics modeling 1.1 Tool motion trajectory mathematical model In order to clarify the condition of the tool in an ideal machining state, three coordinate systems shown in fig. 1 are established based on path planning information, wherein the first coordinate system is a feeding coordinate system O-X fYfZf, the second coordinate system is a main axis coordinate system O-X sYsZs, the third coordinate system is a workpiece coordinate system O w-XwYwZw, and a point O is the center of a ball end mill for path planning. In the coordinate system O-X fYfZf, the axis Z f is perpendicular to the workpiece machining plane, the axis X f coincides with the path planned feed direction, the spindle coordinate system O-X sYsZs can be obtained by tool rake and side rake rotations X f and Y f, the axis Z t coincides with the planned tool axis, and the coordinate system O w-XwYwZw can be obtained by translating O-X fYfZf from O to O w. A tool coordinate system O-X tYtZt is established, and the tool coordinate system O-X tYtZt and the spindle coordinate sys