CN112347585B - Analytical calculation method for contact area between ball end mill and workpiece - Google Patents
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Abstract
The invention relates to the technical field of machine manufacturing, in particular to a method for analyzing and calculating a contact area between a ball end mill and a workpiece, which comprises the following steps: interpolation fitting is carried out through a B spline method to obtain a model of the blade, and cutting positions and geometric parameter files are obtained; according to the condition of chip formation, considering the curvature of the free-form surface, and obtaining the geometric condition limitation of the parametric cutting area; at [0, R]Searching for the ordinate z satisfying the geometric constraint in the interval 1 As the lower limit of the contact area, the upper limit of the contact area is found by a dichotomy, and the contact area [ z ] is finally determined 1 ,z 2 ]. The invention provides a method for analyzing and calculating a contact area between a ball end mill and a workpiece, which solves the problems of large calculated amount and low calculation efficiency of the existing method for acquiring the free-form surface contact area.
Description
Technical Field
The invention relates to the technical field of machine manufacturing, in particular to a method for analyzing and calculating a contact area between a ball end mill and a workpiece.
Background
The free-form surface thin-wall part is widely applied to the industries of aerospace, automobiles, molds and the like. The thin-wall part has the characteristics of thin wall, low rigidity, large curvature and the like, and the problems of flutter, processing deformation and the like are easy to occur in the processing process. These problems are closely related to cutting forces, and accurate acquisition of the tool workpiece contact area is critical to accurately predicting cutting forces during free-form surface machining. At present, an analytic method, a Z-map method and an entity method are mainly adopted for acquiring the free-form surface contact area. The swept body of the cutter and the processed workpiece by adopting the entity method and the Z-map method need to be updated in each calculation, so that the calculated amount is large, the calculation efficiency is low, and the effect of being applied to actual processing is not ideal. The analysis method simplifies the actual processing conditions and can generate calculation errors.
Disclosure of Invention
The invention provides a method for analyzing and calculating a contact area between a ball end mill and a workpiece, which aims to solve the problems of large calculated amount and low calculation efficiency of the existing method for acquiring a free-form surface contact area.
The technical scheme for solving the problems is as follows: the method for analyzing and calculating the contact area of the ball end mill and the workpiece is characterized by comprising the following steps:
s1: reading cutting position and curvature information of a designated tool point from the cutting position and geometry parameter file;
s2: establishing a global coordinate system O g -X g Y g Z g Tool coordinate system O t -X t Y t Z t And a workpiece coordinate system O w -X w Y w Z w Wherein the global coordinate system is a processing coordinate system, the tool coordinate system takes the tool point as the origin, X t Is the projection of the feed direction on the horizontal plane, Z t Is the vector direction of the cutter shaft, and determines Y according to the right-hand rule of a Cartesian coordinate system t In the object coordinate system, X w Is the feed direction, Z w Is the normal direction of the curved surface;
s3: determining a coordinate system transformation relation;
s4: determining geometric limitation conditions of the parametric cutting area according to the curvature of the curved surface and the conditions of chip formation;
s5: determining a lower limit of the contact area;
s6: and obtaining the boundary of the contact area by adopting a dichotomy according to the lower limit of the contact area.
Preferably, it is: the step S1 further includes:
and constructing a ball end mill curved surface machining area calculation model, setting machining process parameters, calculating geometric parameters of a cutter path and a curved surface, and outputting cutting positions and geometric parameter files comprising cutter points, cutter shaft vectors, contact point curvatures and normal vectors.
Preferably, it is: the step of constructing a ball end mill curved surface machining area calculation model specifically comprises the following steps: and carrying out interpolation fitting by a B spline method according to the initial blade vertex and blade root point data to obtain a blade model.
Preferably, it is: the step S3 specifically includes:
any point on the edge line of the cutter is Q, which is O t -X t Y t Z t Is [ x ] 1 ，y 1 ，z 1 ] T And has:
wherein,representing z 1 When=0, the angle θ between the tangent of the blade line and the x-axis of the coordinate is O t -X t Y t Z t The lead angle of the blade line is l, the induced lead P is
Let O be t -X t Y t Z t And O w -X w Y w Z w The transformation matrix between is M t Then Q is at O w -X w Y w Z w Inner coordinates [ x ] 2 ，y 2 ，z 2 ] T Satisfy the following requirements
[x 2 ，y 2 ，z 2 ] T ＝M t [x 1 ，y 1 ，z 1 ] T 。
Preferably, it is: the step S4 specifically includes:
according to the curvature ρx and ρy of the curved surface in the x and y directions and the condition of chip formation, the geometric constraint that the coordinate of the Q point in the parametric region should satisfy is:
preferably, it is: the step S5 specifically includes:
s501: setting calculation precision;
s502: ball end portion [0, R of ball end mill according to calculation accuracy]Discretized into n parts, denoted as z S Let z S ＝z 1 ；
S503: calculating z according to edge line equation 1 Coordinates in the tool coordinate system [ x ] 1 ，y 1 ，z 1 ]By transforming matrix M t Transform it into [ x ] in the local coordinate system of the workpiece 2 ，y 2 ，z 2 ]；
S504: traversal judgment z S Each point [ x ] 2 ，y 2 ，z 2 ]Determining whether the geometry of the reference cut region is satisfied, determining the lower limit z of the contact region 1 。
Preferably, it is: the step S6 specifically includes:
s601: in interval [ z 1 ，R]Searching the upper limit of the parameter cutting area by adopting a binary search algorithm in the interval to ensure that z 2 ＝(z 1 +R)/2, and setting a specified error limit delta;
s602: judgment of z 2 Whether or not it satisfies |z 2 -z 1 |delta, if |z 2 -z 1 And calculating z according to the edge line equation 2 Coordinates in the tool coordinate system [ x ] 1 ，y 1 ，z 1 ]By transforming matrix M t Transform it into [ x ] in the local coordinate system of the workpiece 2 ，y 2 ，z 2 ]；
S603: judgment [ x ] 2 ，y 2 ，z 2 ]Whether the geometric conditions of the parametric region are satisfied, if so, z 2 ＝(z 2 +R)/2, repeating the judgment of |z 2 -z 1 |＞δ；
S604: repeating steps S602 and S603, when |z 2 -z 1 I < delta or [ x ] 2 ，y 2 ，z 2 ]Outputting the tangent region boundary [ z ] when the geometric constraint of the tangent region is not satisfied 1 ，z 2 ]。
Compared with the prior art, the invention has the beneficial effects that: according to the invention, a blade model is generated in CAM software according to the original data points, the cutting position and geometric parameter data of the blade model are extracted, the contact area between the ball end milling cutter and the workpiece in the free-form surface machining process is calculated by adopting an analytic method, the calculation efficiency is improved, the influence of the curvature of the free-form surface is considered, and the calculation result is more accurate compared with the existing analytic method. The method has important significance for rapidly judging the cutting state of the cutting edge, accurately predicting the cutting force and processing simulation.
Drawings
FIG. 1 is a flow chart of the calculation of the contact area of a ball nose milling cutter with a workpiece during free-form surface machining;
FIG. 2 is a blade finishing tool point;
FIG. 3 is a relationship between various coordinate systems;
FIG. 4 is a three-dimensional model of an adjacent cutter point chip forming process;
FIG. 5 is a three-dimensional model of an adjacent tool path chip forming process;
FIG. 6 is a model of a solution of geometric constraints for adjacent tool bit contact areas;
FIG. 7 is a geometric constraint solution model of adjacent tool path contact areas;
fig. 8 is a comparison of resolving milling forces by an analytical method taking into account curvature of a curved surface with a conventional analytical method.
Reference numerals: 1-a global coordinate system, 2-a workpiece coordinate system, 3-a tool coordinate system, 4-an adjacent tool position condition, 5-an adjacent tool path condition, 6-a common analysis method and 7-an analysis method considering curved surface curvature.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention.
Example 1: the method for analyzing and calculating the contact area between the ball end mill and the workpiece, as shown in fig. 1-8, avoids a large amount of calculation in the process of updating the cutter swept body and processing the workpiece each time, improves the calculation efficiency, and simultaneously considers the influence of the curvature of the free curved surface and improves the calculation precision compared with the traditional analyzing method. The method is suitable for judging the instantaneous contact area in the process of machining the free-form surface by the ball end mill, and can be used for predicting the cutting force in the process of milling the free-form surface. The specific implementation steps are as follows:
step 1: according to the initial blade vertex and blade root point data, obtaining a blade model through interpolation fitting by a B spline method, and selecting a ball end milling cutter as a processing cutter; and inputting a cutter radius R, setting processing technological parameters according to requirements, calculating geometric parameters of a cutter path and a curved surface in CAM software, and outputting cutting positions and geometric parameter files comprising a cutter point, a cutter axis vector, a contact point curvature and a normal vector. Blade finishing tool locations are shown in fig. 2.
Step 2: as shown in fig. 3, a global coordinate system 1 (O g -X g Y g Z g ) Tool coordinate System 2 (O) t -X t Y t Z t ) And a workpiece coordinate system 3 (O w -X w Y w Z w ). The global coordinate system 1 is a machining coordinate system. The tool coordinate system 2 takes the tool point as the origin, X t Is the projection of the feed direction on the horizontal plane, Z t Is the vector direction of the cutter shaft, and determines Y according to the right-hand rule of a Cartesian coordinate system t . In the object coordinate system 3, X w Is the feed direction, Z w Is the normal of the curved surface.
Step 3: the relation between the coordinate systems can be used for solving the coordinates of any point Q on the cutter edge line in each coordinate system. Any point Q on the edge line, which is at O t -X t Y t Z t Is [ x ] 1 ，y 1 ，z 1 ] T And has:
wherein,representing z 1 At=0, the tangent to the blade line forms an angle with the x-axis of the coordinate. Theta is O t -X t Y t Z t The lead angle of the blade line is l, the induced lead P is
Let O be t -X t Y t Z t And O w -X w Y w Z w The transformation matrix between is M t Then Q is at O w -X w Y w Z w The coordinates within satisfy:
[x 2 ，y 2 ，z 2 ] T ＝M t [x 1 ，y 1 ，z 1 ] T 。
step 4: considering the curvatures ρx and ρy of the curved surface in the x and y directions, according to the condition of chip formation, the geometric constraint that the coordinate of the Q point in the parametric region should satisfy is:
wherein a is p For axial depth of cut Y, Z is the Y, Z coordinates of the center of sphere of fun2 in fig. 5 obtained from geometric relationships.
In FIG. 6, the adjacent cutter position 4 is shown with fun1 at feed f z The direction, i-th tool position and i+1-th tool position are cut by a boundary line, and the geometric constraint condition is that z is less than or equal to a p And solving a fun1 equation according to the geometric condition to obtain the geometric limitation of the x direction and the z direction, wherein x is more than or equal to fun 1. The adjacent tool path case 5 in fig. 7 is: fun2 is a circular cutting boundary formed by the radial ith tool position point and the i+1 tool position points, and the geometric limitation in the y direction can be obtained by solving a Fun2 equation according to geometric conditions.
Step 5: first find the lower bound z of the contact area 1 According to the requirement of calculation accuracy, ball head parts [0, R of ball head milling cutter]Discretized into n parts, denoted as z S Let z S ＝z 1 According to the edge line equationCalculating z 1 Coordinates in the tool coordinate system [ x ] 1 ，y 1 ，z 1 ]By transforming matrix M t Transform it into [ x ] in the local coordinate system of the workpiece 2 ，y 2 ，z 2 ]Traversing and judging z S Each point [ x ] 2 ，y 2 ，z 2 ]Determining the lower bound z of the contact region if the geometry of the reference region is satisfied 1 。
Step 6: with a defined lower limit z of the contact area 1 As input, determine interval [ z ] 1 ，R]Searching the upper boundary of the contact area by adopting a binary search algorithm in the interval to enable z 2 ＝(z 1 +R)/2。
For a given error limit delta, if |z 2 -z 1 And calculating z according to the edge line equation 2 Coordinates in the tool coordinate system [ x ] 1 ，y 1 ，z 1 ]By transforming matrix M t Transform it into [ x ] in the local coordinate system of the workpiece 2 ，y 2 ，z 2 ]Judging whether the geometric conditions of the parameter cutting area are met, if yes, z 2 ＝(z 2 +R)/2, repeating the judgment of |z 2 -z 1 I > delta, and when not satisfied, output [ z ] 1 ，z 2 ]。
Step 7: repeating the step 6, when |z 2 -z 1 I < delta or [ x ] 2 ，y 2 ，z 2 ]When the geometric constraint of the parametric region is not satisfied, output [ z ] 1 ，z 2 ]。
The method is used for verifying the correctness: the contact area is determined by adopting a contact area which is solved by considering a curved surface curvature analysis method 7 and a common analysis method 6 respectively 1 ，z 2 ]As an integration interval of the cutting resultant force, the cutting force during one rotation of the tool at the selected point is solved. As shown in fig. 8, it can be seen from the figure that the curvature of the considered curved surface and the curvature of the non-considered curved surface have good consistency in most areas, and only the difference occurs at the end point during one rotation of the tool, which indicates that the curvature of the considered curved surface affects the cutting force.
Example 2: a method for analyzing and calculating contact area between ball-end milling cutter and workpiece features that the initial blade vertex and blade root point data are used to generate blade in CMA software as the finishing target, the 30 th row of tool track is chosen, and the 50 th tool position is used to calculate the instantaneous contact area between ball-end milling cutter and workpiece. The analytical calculation method is shown in fig. 1, and comprises the following steps:
1. the object of the processing in this example is a blade obtained by CAM software, the tool being a ball end mill, the tool radius r=3mm.
And setting processing technological parameters according to requirements, calculating geometric parameters of a cutter path and a curved surface in CAM software, and outputting cutting positions and geometric parameter files comprising a cutter point, a cutter axis vector, a contact point curvature and a normal vector.
2. And reading and selecting the cutting position and curvature information of the 30 th row of tool paths and the 50 th tool point from the cutting position and geometric parameter file.
The cutter shaft vector is [29.6716,1.2358, -3.4783 ]]Contact point curvature ρx=0.0071, ρy= 0.00306, contact point coordinates [51.3475, 27.3192, -16.5602]Passing the coordinates through a transformation matrix M t Transformed into the workpiece coordinate system, the coordinates are [55.2106, -20.8711, 13.1685]。
3. According to the precision requirement delta=0.01, the ball head parts [0,3 ] of the ball head cutter are]Discrete 300 parts, recorded as array z S Find z S A lower boundary z of the contact region which is the point satisfying the geometry of the cutting region 1 。
4. With a defined lower limit z of the contact area 1 As input, determine interval [ z ] 1 ，R]Searching the upper boundary of the reference cutting area by adopting a binary search algorithm in the interval to ensure that z 2 ＝(z 1 +R)/2。
If |z 2 -z 1 And calculating z according to the edge line equation 2 Coordinates in the tool coordinate system [ x ] 1 ，y 1 ，z 1 ]By transforming matrix M t Transform it into [ x ] in the local coordinate system of the workpiece 2 ，y 2 ，z 2 ]Judging whether the geometric conditions of the parameter cutting area are met, if yes, z 2 ＝(z 2 +R)/2, repeating the judgment of |z 2 -z 1 I > delta, and when not satisfied, output [ z ] 1 ，z 2 ]。
5. Repeating the step 4, when |z 2 -z 1 I < delta or [ x ] 2 ，y 2 ，z 2 ]When the geometric constraint of the parametric region is not satisfied, output [ z ] 1 ，z 2 ]。
According to the invention, the influence of the curvature of the free curved surface is considered, the contact area of the cutter workpiece is calculated by adopting an analytic method, so that the calculation efficiency is improved compared with an entity method and a Z-map method, and the calculation precision is improved compared with the traditional analytic method.
The foregoing description is only exemplary embodiments of the present invention, and is not intended to limit the scope of the present invention, and all equivalent structures or equivalent processes using the descriptions and the drawings of the present invention, or direct or indirect application in other related system fields are included in the scope of the present invention.
Claims (3)
1. The method for analyzing and calculating the contact area between the ball end mill and the workpiece is characterized by comprising the following steps:
s1: reading cutting position and curvature information of a designated tool point from the cutting position and geometry parameter file;
s2: establishing a global coordinate system O g -X g Y g Z g Tool coordinate system O t -X t Y t Z t And a workpiece coordinate system O w -X w Y w Z w Wherein the global coordinate system is a processing coordinate system, the tool coordinate system takes the tool point as the origin, X t Is the projection of the feed direction on the horizontal plane, Z t Is the vector direction of the cutter shaft, and determines Y according to the right-hand rule of a Cartesian coordinate system t In the object coordinate system, X w Is the feed direction, Z w Is the normal direction of the curved surface;
s3: the step S3 of determining a coordinate system transformation relationship specifically includes:
any point on the edge line of the cutter is Q, which is O t -X t Y t Z t Is [ x ] 1 ,y 1 ,z 1 ] T And has:
wherein,representing z 1 When=0, the angle between the tangent of the blade line and the x-axis of the coordinate, R is the radius of the tool, θ is O t -X t Y t Z t The lead angle of the blade line is l, the induced lead P is
Let O be t -X t Y t Z t And O w -X w Y w Z w The transformation matrix between is M t Then Q is at O w -X w Y w Z w Inner coordinates [ x ] 2 ,y 2 ,z 2 ] T Satisfy the following requirements
[x 2 ,y 2 ,z 2 ] T ＝M t [x 1 ,y 1 ,z 1 ] T ；
S4: determining geometric constraints of the parametric region according to the curvature of the curved surface and the conditions of chip formation, wherein the step S4 specifically comprises:
according to the curvature ρx and ρy of the curved surface in the x and y directions and the condition of chip formation, the geometric constraint that the coordinate of the Q point in the parametric region should satisfy is:
wherein R is the radius of the tool, ρx is the curvature of the curved surface in the x direction, a p Is axial cutting depth;
s5: determining the lower limit of the contact area, wherein the step S5 specifically includes:
s501: setting calculation precision;
s502: ball end portion [0, R of ball end mill according to calculation accuracy]Discretized into n parts, denoted as z S Let z S ＝z 1 ；
S503: calculating z according to edge line equation 1 Coordinates in the tool coordinate system [ x ] 1 ,y 1 ,z 1 ]By transforming matrix M t Transform it into [ x ] in the local coordinate system of the workpiece 2 ,y 2 ,z 2 ]；
S504: traversal judgment z S Each point [ x ] 2 ,y 2 ,z 2 ]Determining whether the geometry of the reference cut region is satisfied, determining the lower limit z of the contact region 1 ；
S6: according to the lower limit of the contact area, a dichotomy is adopted to obtain the boundary of the contact area, and the step S6 specifically comprises:
s601: in interval [ z 1 ,R]Searching the upper limit of the parameter cutting area by adopting a binary search algorithm in the interval to ensure that z 2 ＝(z 1 +R)/2, and setting a specified error limit delta;
s602: judgment of z 2 Whether or not it satisfies |z 2 -z 1 |>Delta, if |z 2 -z 1 |>Delta, then calculate z according to the edge line equation 2 Coordinates in the tool coordinate system [ x ] 1 ,y 1 ,z 1 ]By transforming matrix M t Transform it into [ x ] in the local coordinate system of the workpiece 2 ,y 2 ,z 2 ]；
S603: judgment [ x ] 2 ,y 2 ,z 2 ]Whether the geometric conditions of the parametric region are satisfied, if so, z 2 ＝(z 2 +R)/2, repeating the judgment of |z 2 -z 1 |>δ；
S604: repeating steps S602 and S603, when |z 2 -z 1 |<Delta or [ x 2 ,y 2 ,z 2 ]Outputting the tangent region boundary [ z ] when the geometric constraint of the tangent region is not satisfied 1 ,z 2 ]。
2. The method for analyzing and calculating the contact area between a ball nose milling cutter and a workpiece according to claim 1, wherein the step S1 further comprises:
and constructing a ball end mill curved surface machining area calculation model, setting machining process parameters, calculating geometric parameters of a cutter path and a curved surface, and outputting cutting positions and geometric parameter files comprising cutter points, cutter shaft vectors, contact point curvatures and normal vectors.
3. The method for analyzing and calculating the contact area between the ball end mill and the workpiece according to claim 2, wherein the constructing the curved surface processing area calculation model of the ball end mill specifically comprises: and carrying out interpolation fitting by a B spline method according to the initial blade vertex and blade root point data to obtain a blade model.
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| WO2012153157A2 (en) * | 2011-05-09 | 2012-11-15 | Pécsi Tudományegyetem | Method for optimizing cutting forces in a milling process and computer-controlled milling machine using the same method |
| CN111026035A (en) * | 2019-12-26 | 2020-04-17 | 山东大学 | Method for solving cyclone milling blade tool location point based on curvature change |
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