A method for optimizing the tool shaft vector of a face milling cutter

Abstract

The application discloses a kind of flat bottom end face milling cutter tool shaft vector optimization method, tool shaft vector optimization is considered from processing interference, cutting force, rotation axis angular displacement and angular velocity etc. Multiple factors comprehensively. First, the improved space partition tool shaft vector global interference detection method based on surface principle is proposed, whether the interference detection algorithm is used to judge tool to occur processing interference and carry out interference-free tool shaft vector space calculation;Second, the relationship model of end milling cutter tool shaft vector and cutting force change is established, and the tool shaft vector optimization is carried out with the tool cutting force optimization as the target;Third, using Dijkstra algorithm, an optimal path algorithm-based machine tool rotation axis angular displacement and angular velocity optimization model is proposed;Using the optimization algorithm for complex surface machining, the machining quality of the surface workpiece after tool shaft vector optimization is obviously improved compared with that before tool shaft vector optimization.

Description

Technical Field

[0001] This invention relates to a vector optimization method for milling cutter axes, and more particularly to a vector optimization method for milling cutter axes that comprehensively considers multiple factors such as machining interference, cutting force, rotation axis angular displacement and angular velocity, belonging to the field of machining technology. Background Technology

[0002] In five-axis machining, existing tool axis vector optimization methods only consider the interference between the tool and the workpiece, and are only applicable to ball end mills, which has significant limitations. Tool axis vector optimization should comprehensively consider multiple factors such as machining interference, cutting force, rotary axis angular displacement, and angular velocity. Summary of the Invention

[0003] To overcome the interference problem in the prior art, this invention proposes a method for optimizing the tool axis vector of a flat-bottom end mill, which includes the following steps:

[0004] Step 1: Calculation of the tool axis vector space without interference

[0005] During the machining process, if the projections of the machine tool slide and the workpiece are tangent or intersecting, it is considered interference. The specific judgment method is as follows:

[0006] Let S be the projected profile of the surface to be machined along the Z-axis of the workpiece coordinate system. Divide S into n equidistant infinitesimal elements with a distance ε. Then the endpoints of the equidistant infinitesimal elements are represented as [S1, S2, S3...S...]. n Let R be the projected profile of the machine tool slide along the Z-axis of the workpiece coordinate system. Divide R into m equidistant infinitesimal elements with a distance ε. Then the endpoints of the equidistant infinitesimal elements are represented as [R1, R2, R3...R...]. m ].

[0007] The coordinates of the endpoints of two adjacent infinitesimal elements on the projected contour S are defined as follows: The coordinates of the endpoints of two adjacent infinitesimal elements on the projected contour R are defined as follows: u and v are directed line segment vectors, such as Figure 1 As shown.

[0008] like Figure 1 As shown, directed line segment S j S i+1 and R j R i+1 If they intersect, then:

[0009]

[0010] By calculating the x and y coordinates in equation (1) respectively, we can obtain:

[0011]

[0012] Solving the equation set, we get:

[0013]

[0014] Two directed line segments if there is intersection point, then 0≤u≤1 and 0≤v≤1, otherwise there is no intersection point.

[0015] Regarding the calculation of the micro-element end point coordinates of the projection S and the projection R in the workpiece coordinate system, since the projection S is fixed relative to the workpiece coordinate system, the coordinates of the micro-element end points are also fixed and do not need to be calculated separately. However, the position of the projection R changes constantly due to the movement of the machine tool, so the calculation of the micro-element end point coordinates of the projection R in the workpiece coordinate system is required.

[0016] Define the micro-element end point of the projection R The distance between the micro-element end point of the projection R and the origin of the machine tool ram (Z-axis) local coordinate system is It can be obtained that after all the micro-element end points of the ram projection R are obtained, the intersection calculation is performed by traversing all the micro-element end points of the projection S and the projection R. If the number of intersection points is greater than or equal to 1, it means that the projection has interference, and if there is no intersection point, it means that there is no interference. In general, the rotation axis of the machine tool is not infinite, and the five-axis machine tool is set as XYZAC form, with the A and C axes having rotation limits of -90° to 90° and -360° to 360°, respectively. The optimization of the tool axis vector also has certain constraints. When performing interference checking on the tool axis vector, 0.001 ° is taken as the minimum unit, and then according to the degree combinations within the rotation ranges of the A and C axes, the interference-free tool axis vector range is obtained by searching.

[0017] Step 2: Flat-end mill tool axis vector optimization based on optimal cutting force

[0018] Divide the cutting edge of the flat-end mill blade into M micro-elements in the axial direction. The instantaneous cutting force model expression of the cutting edge micro-element in the radial, tangential, and axial directions at time T in the cutting edge micro-element coordinate system is:

[0019]

[0020] (4) In the formula, g(φ ij ) is a unit step function used to indicate whether the current cutting edge is involved in cutting; df r is the radial cutting force micro-element; df t is the tangential cutting force micro-element; df a is the axial cutting force micro-element; K rc is the radial shear force coefficient; Ktc Tangential shear force coefficient; K ac These are the radial, tangential, and axial shear force coefficients, respectively; K te K is the radial tillage force coefficient. re K represents the tangential plowing force coefficient. ae h is the axial plowing force coefficient. z dz is the instantaneous undeformed chip thickness; ds is the element height; ds is the element cutting edge length.

[0021] Based on the principle of coordinate transformation, the resultant cutting force in the X, Y, and Z directions for a certain infinitesimal element j on the cutting edge i is obtained as follows:

[0022]

[0023] Let the total number of inserts on the milling cutter head be N, and each insert be subdivided into M infinitesimal elements. By integrating along the axial direction and summing the cutting forces on all the inserts on the cutter head, the cutting force at a certain instant T can be obtained as follows:

[0024]

[0025] Finally, the triaxial combined cutting force can be obtained as follows:

[0026]

[0027] In actual multi-axis machining of parts, the chips generated are produced by the milling cutter's cutting edge repeatedly cutting into and out of the workpiece blank material, with an instantaneous, undeformed chip thickness h. z Defined as an irregular polyhedral structure formed by the surface of the unmachined part, the envelope of the previous cutting edge, the tool path, and the envelope of the current cutting edge.

[0028] Instantaneous undeformed chip thickness h z The calculation method is as follows: When a certain cutting point on the cutting edge extends along the outward normal vector direction and reaches the previous cutting edge, the cutting point P of the cutting edge... t Intersection point P with the previous blade t-Δt Distance between |P t P t-Δt This refers to the undeformed cutting thickness. For example... Figure 2 As shown, the blade sweep trajectory is circular, and the thickness is the cutting depth a. p .

[0029] Passing through point P t and point P t-Δt The parametric equation of line l is expressed as:

[0030]

[0031] Point Pt The coordinates of point P t,x t,y t,z are represented as (P t-Δt , P x0 , P y0 ) in the tool coordinate system. The swept cylindrical surface of the i-1th blade where point P z0 is located is represented as Q in the tool coordinate system, the coordinates of the center of the base circle of the surface are (Q x' , Q y' , Q z' ), and the axial direction vector of the cylinder is R'(r t-Δt , r t , r t-Δt ). Then Q is represented as:

[0032]

[0033] Equations (5) and (6) are solved simultaneously to obtain the coordinates of point P t-Δt in the workpiece coordinate system. The simultaneous equations may have multiple solutions because the intersection of a straight line and a cylindrical surface may be two. In this case, the coordinates of P t are obtained that make |P t-Δt P t-Δt | minimum, and the instantaneous undeformed chip thickness h z is obtained from this.

[0034] Step three: tool axis vector smoothing optimization algorithm based on machine tool kinematics

[0035] The coordinates of the end of the tool axis to be optimized at a point D i on the tool contact point trajectory are set as (D ix , D iy , D iz ). According to the machine tool kinematics coordinate transformation, the rake angle φ α and the inclination angle φ β are converted into the angular displacements A i and C i of the machine tool A-axis and C-axis. Then the coordinates of the end of the optimized tool axis (D ix' , D iy' , D iz' ) can be represented as:

[0036]

[0037] After obtaining the coordinates of the end of the optimized tool axis, the rotational axis displacement from point D i-1 to point D i can be represented as:

[0038]

[0039] Since D iThere are many choices for the point, and the objective function based on the optimization of the rotation axis angular displacement can be expressed as:

[0040]

[0041] However, only calculating the optimal rotation axis angular displacement cannot completely ensure smoother machine tool movement, because the movement of the machine tool is inherently characterized by the maximum rotation axis angular velocity allowed by the machine tool. Therefore, the angular velocity of the rotation axis also needs to be controlled.

[0042] The machine tool rotation axis angular displacement solution, as a typical single-source shortest path algorithm, can be solved using the greedy algorithm, i.e., the Dijkstra algorithm, which can better solve the shortest path from one vertex to the remaining vertices. Assuming that each feasible tool axis vector is a vertex in the directed graph, and each vertex belongs to a unique set, the vertices in adjacent sets can be arbitrarily associated. After establishing the directed graph, the connectivity of the initial tool axis vector and each tool axis vector at the end of the tool contact point trajectory is detected. The solution of the global minimum optimization model for the tool axis vector change amount can be simplified as finding the shortest path from the initial tool axis vector to all tool axis vectors at the end of the tool contact point, and comparing the weight sums of all shortest paths to find the minimum one. The tool axis vector on this path is the optimal tool axis vector sequence we are looking for.

[0043] As shown in Figure 3 , the tool contact point set D has a total of k tool contact points, each of which has a machine tool rotation axis feasible region constructed using the above step one. Assuming that the optimal tool axis vector combination of tool contact point D1 is A1, C1, D2, the optimal tool axis vector combination of tool contact point C2 is A2, C2, D i , and the optimal tool axis vector combination of tool contact point D3 is A i , C i , then before the optimal tool axis vector combination is found, a tool axis vector group consisting of discrete points forming the tool path needs to be found in each machine tool rotation axis feasible region with the minimum machine tool rotation axis compound angular displacement as the objective function.

[0044] Since the initial construction of the tool axis vector group has low machine tool rotation axis feasible region division precision, a new machine tool rotation axis feasible region is constructed in the vicinity of the selected grid discrete points of each tool contact point machine tool rotation axis, and grid division is performed again. The Dijkstra algorithm is applied to find the optimal tool axis vector group, and the above steps are repeated multiple times until the machine tool rotation axis compound angular displacement and the kinematic characteristics of the machine tool do not change significantly or the iteration condition is reached, and the algorithm operation is terminated. The overall process is shown in Figure 4 , which has higher computational efficiency than other shortest path solving methods.

[0045] Step four: multi-factor based tool axis vector optimization model establishment

[0046] (1) Objective function

[0047] According to step one-step three, the cutting force F0 and the rotation axis angular displacement L i is defined as the objective function, and thus the surface milling optimization target is obtained:

[0048]

[0049] When performing optimization solving, it is often difficult to achieve multiple objectives simultaneously optimal, and thus the formula can be rewritten as:

[0050] minW(φ α , φ β ) = w1L i + w2F0 (12)

[0051] In the formula, w1 and w2 are weight coefficients of the rotation axis angular displacement and the cutting force respectively, and w1+w2=1. The weight of each target can be determined by fuzzy evaluation method, expert scoring method, etc.

[0052] (2) Constraint condition

[0053] When performing optimization of the objective function, the rake angle and the roll angle combination that has global interference and rotation axis angular velocity exceeding the maximum limit value need to be removed.

[0054] Compared with the prior art, the method proposed in the patent comprehensively considers machining interference, cutting force, rotation axis angular displacement and angular velocity to optimize the tool axis vector. The existing methods often only optimize one aspect and ignore other aspects. The machining quality of the complex surface workpiece after optimization of the tool axis vector is significantly improved compared with that without optimization of the tool axis vector. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 Projection diagram of machine tool ram and surface to be machined.

[0056] Figure 2 Simple diagram of undeformed chip thickness of flat bottom face milling cutter.

[0057] Figure 3 Schematic diagram of feasible region discretization and shortest path solving.

[0058] Figure 4 Schematic diagram of using Dijkstra algorithm to optimize machine tool rotation axis.

[0059] Figure 5The schematic diagram of the curved surface to be machined.

[0060] Figure 6 The schematic diagram of the cutting area division and the tool axis vector in various cases; (a) the division of the machining overlapping area.

[0061] (b) the tool axis vector without considering the interference, all using normal machining, and collision will occur when machining to the interference area.

[0062] (c) the optimization of the tool axis vector considering only the machining interference.

[0063] (d) the tool axis vector planning considering the interference avoidance, cutting force, rotation axis angular displacement and angular velocity, compared with (b), the smooth tool axis vector and the avoidance of interference are maintained without changing the tool contact point trajectory.

[0064] Figure 7 The comparison of the rotation axis angular displacement before and after the optimization of the tool axis vector.

[0065] Figure 8 The comparison of the rotation axis angular velocity of A and C before and after the optimization. DETAILED DESCRIPTION

[0066] The simulation and experimental machining verification are carried out on a large-scale ship propeller scale-down part, the propeller model is simplified, only two blades are reserved, and the tool needs to avoid collision with the interference surface when cutting the curved surface to be machined. The workpiece established is shown in Figure 5 .

[0067] The division of the interference area and the non-interference area of the propeller curved surface to be machined based on step one is shown in Figure 6 (a), Figure 6 (b) is the tool axis vector planning of the curved surface without considering the interference avoidance, if machining is carried out according to this method, global interference will occur at the tool contact point in the interference area. Figure 6 (c) is the tool axis vector planning considering only the interference avoidance, without considering the cutting force and the rotation axis angular displacement and angular velocity, if machining is carried out according to this method, although global interference can be avoided, the cutting force and the rotation axis angular velocity will suddenly increase at a certain moment, affecting the machining quality of the workpiece. Figure 6 (d) is the tool axis vector planning considering the interference avoidance, cutting force, rotation axis angular displacement and angular velocity, it can be seen from the figure that, compared with the tool axis vector planning considering only the interference avoidance, the smooth rotation axis trajectory is obtained in the whole tool path interval, and the sudden increase of the cutting force and the rotation axis angular displacement will not be caused.

[0068] The comparison of the rotation axis angular displacement before and after the optimization is shown in Figure 7The trajectory is only considered interference avoidance, the trajectory line before the optimization of the rotation axis angular displacement, and the trajectory is the trajectory line after the optimization of the rotation axis angular displacement. As can be seen from the figure, there is a trajectory mutation in the trajectory line before the optimization, which will cause the sudden increase of the rotation axis angular velocity, and affect the machining quality. At the same time, the total length of the rotation axis angular displacement trajectory line after the Dijkstra optimization algorithm is 254.8mm, and the total length of the trajectory line before the optimization is 274.5mm. The optimized angular displacement is shortened by 7.18% compared with that before the optimization.

[0069] From Figure 8 It can be seen that the overall tool axis vector optimization and construction of the tool path of the above parameter surface to be optimized is better than the conventional tool axis vector construction method using commercial CAM software in terms of machine tool kinematics performance. Among them, the maximum angular velocity of the machine tool rotation axis A is reduced from 159.06° / s to 17.28° / s; the maximum angular velocity of the C-axis is reduced from 566.31° / s to 66.22° / s, and the rest of the machine tool kinematics characteristics are also better optimized. It can be seen that when the tool axis vector of the flat bottom face milling cutter for complex surface is constructed by using this optimization method, the maximum angular velocity of the machine tool rotation axis is obviously reduced, which theoretically improves the quality of five-axis machining of complex surfaces.

Claims

1. A method for optimizing the cutter axis vector of a flat-bottom end mill, characterized in that, The method includes the following steps: Step 1: Calculation of the tool axis vector space without interference; During the machining process, if the projections of the machine tool slide and the workpiece are tangent or intersecting, it is considered interference. The specific judgment method is as follows: Let the surface to be machined be along the workpiece coordinate system The projected profile of the axis is ,Will Divided into The distance is If the equidistant infinitesimal elements are given, then the endpoints of the equidistant infinitesimal elements are represented as follows: Assume the machine tool slide is along the workpiece coordinate system. The projected profile of the axis is ,Will Divided into The distance is If the equidistant infinitesimal elements are given, then the endpoints of the equidistant infinitesimal elements are represented as follows: ; Defined in the projected profile The coordinates of the two adjacent endpoints of the infinitesimal element are ( , ); ( , ), defined in the projected profile The coordinates of the two adjacent endpoints of the infinitesimal element are ( , ); ( , ), It is a directed line segment vector; Directed line segment and If they intersect, then: (1)； Calculate the x and y coordinates in equation (1) respectively, and obtain: (2)； Solving the system of equations, we obtain: (3)； If two directed line segments intersect, then and ; For projection The coordinates of the endpoints of the infinitesimal element in the workpiece coordinate system are calculated. Step 2: Optimize the cutter axis vector of the flat-bottom end mill based on the optimal cutting force; Along the axial direction, the cutting edge of the flat-bottom end mill insert is subdivided into... A microelement, in The instantaneous cutting force model expression of the cutting edge element at time t is as follows in the coordinate system of the cutting edge element: The cutting forces in the radial, tangential, and axial directions at time t are: (4)； (4) In the formula, This is a unit step function used to indicate whether the current cutting edge is participating in cutting; The radial cutting force is a micro-element. The element is a tangential cutting force micro-element; This is a micro-element of axial cutting force; Radial shear force coefficient; Tangential shear force coefficient; These are the radial, tangential, and axial shear force coefficients, respectively. Radial plowing force coefficient; This is the tangential plowing force coefficient; This is the axial plowing force coefficient; The instantaneous thickness of the undeformed chip; The height of the infinitesimal element; For the length of the infinitesimal blade; Based on the principle of coordinate transformation, the cutting edge is obtained. A certain blade element on it is of , , The resultant cutting force in the direction is: (5)； Let the total number of cutting inserts on the milling cutter head be... Each blade is finely divided into By integrating along the axial direction using a few infinitesimal elements, and summing the cutting forces on all the cutterhead inserts, the instantaneous value can be obtained. The cutting force is: (6)； The final triaxial combined cutting force is: (7)； Instantaneous undeformed chip thickness Defined as an irregular polyhedral structure formed by the surface of the unmachined part, the envelope of the previous cutting edge, the tool path, and the envelope of the current cutting edge; Instantaneous undeformed chip thickness The calculation method is as follows: when a certain cutting point on the cutting edge extends along the outward normal vector direction and reaches the previous cutting edge, the cutting point of the cutting edge... Intersection with the previous blade Distance between This is the undeformed cutting thickness; the tool sweep path is circular, and the thickness is the cutting depth. ; Passing point and points straight line The parametric equation is expressed as: (8)； point The coordinates are represented as In the blade coordinate system, point The first The sweeping cylindrical trajectory surface of each blade is used Let represent the coordinates of the center of the base circle of the curved surface as The axial direction vector of the cylinder is ,but Represented as: (9)； Solving equations (5) and (6) simultaneously yields the point. Coordinates in the workpiece coordinate system , take Get the minimum value The coordinates of the point are used to obtain the instantaneous undeformed chip thickness. ; Step 3: Tool axis vector smoothing optimization algorithm based on machine tool kinematics performance; Set a point on the tool contact trajectory The coordinates of the cutter shaft end point to be optimized are Based on the kinematic coordinate transformation of the machine tool, the forward tilt angle is... and roll angle Convert to machine tool shaft and angular displacement of the axis and The optimized toolshaft end coordinates It can be represented as: (10)； After obtaining the optimized coordinates of the cutter shaft end, point Time The rotational angular displacement is expressed as: (11)； because There are multiple choices of points, and the objective function based on the rotation axis angular displacement optimization can be expressed as: (12)； Control the angular velocity of the rotating shaft; Step 4: Establishment of a multi-factor tool axis vector optimization model; (1) Objective function; Based on steps one through three, the cutting force and rotational angular displacement Defined as the objective function, the optimization objective for surface milling can be obtained as follows: (13)； When performing optimization, it is often difficult to achieve the optimal results for multiple objectives simultaneously. Therefore, the formula can be rewritten as: (12)； In the formula, , These are the weighting coefficients for the rotational axis angular displacement and the cutting force, respectively. (2) Constraints; When optimizing the objective function, combinations of tilt and roll angles that cause global interference or whose rotational axis angular velocity exceeds the maximum limit need to be eliminated.

2. The method for optimizing the cutter axis vector of a flat-bottom end mill according to claim 1, characterized in that, For projection The specific process for calculating the endpoint coordinates of the infinitesimal element in the workpiece coordinate system is as follows: defining the projection. At a certain infinitesimal endpoint ( , The distance between the machine tool slide and the origin of the local coordinate system of the Z-axis is ( The projection of the bolster can be obtained. All infinitesimal endpoints are obtained by traversing the projection. and projection The intersection of all infinitesimal endpoints is calculated. If the number of intersection points is greater than or equal to 1, it indicates that interference has occurred in the projection; if there are no intersection points, it indicates that no interference has occurred.

3. The method for optimizing the cutter axis vector of a flat-bottom end mill according to claim 1, characterized in that, The steps for controlling the angular velocity of the rotary axis are as follows: The angular displacement of the machine tool rotary axis is solved using a greedy algorithm, specifically Dijkstra's algorithm. Each feasible tool axis vector is a vertex in a directed graph, and each vertex uniquely belongs to a set. Vertices in adjacent sets are arbitrarily related. After establishing the directed graph, connectivity is checked between the initial tool axis vector and each tool axis vector at the end point of the tool contact trajectory. Solving the global minimum optimization model for the change in tool axis vectors simplifies to finding the shortest path from the initial tool axis vector to all tool axis vectors at the end point of the tool contact, and comparing the sum of the weights of all shortest paths to find the path with the smallest sum. The tool axis vectors on this path are the optimal tool axis vector sequence. (Tool contact set...) Total There are several tool contacts, each with a feasible region for the machine tool rotation axis constructed using a feasible tool axis vector. Assuming the tool contacts... The optimal tool axis vector combination is , The optimal tool axis vector combination is , The optimal tool axis vector combination is Therefore, before the optimal tool axis vector combination is found, it is necessary to find a discrete point in each feasible region of the machine tool rotation axis for each tool contact point, with the objective function of minimizing the composite angular displacement of the machine tool rotation axis, to form a tool axis vector group for the tool trajectory.

4. The method for optimizing the cutter axis vector of a flat-bottom end mill according to claim 3, characterized in that, In the vicinity of the selected grid discrete points in the initially constructed feasible domain of each tool contact machine tool rotation axis, a new feasible domain of the machine tool rotation axis is constructed, and the grid is divided again. The Dijkstra algorithm is applied to find the optimal tool axis vector set. The above steps are repeated multiple times until the composite angular displacement of the machine tool rotation axis and the kinematic characteristics of the machine tool do not change significantly or the iteration condition is met, at which point the algorithm is terminated.

Images