CN116442012A - Method for calculating grinding track of rotary file with partitioned circular arc head - Google Patents
Method for calculating grinding track of rotary file with partitioned circular arc head Download PDFInfo
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- CN116442012A CN116442012A CN202310235463.5A CN202310235463A CN116442012A CN 116442012 A CN116442012 A CN 116442012A CN 202310235463 A CN202310235463 A CN 202310235463A CN 116442012 A CN116442012 A CN 116442012A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B1/00—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B3/00—Sharpening cutting edges, e.g. of tools; Accessories therefor, e.g. for holding the tools
- B24B3/60—Sharpening cutting edges, e.g. of tools; Accessories therefor, e.g. for holding the tools of tools not covered by the preceding subgroups
- B24B3/607—Sharpening cutting edges, e.g. of tools; Accessories therefor, e.g. for holding the tools of tools not covered by the preceding subgroups of files
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract
The invention discloses a method for calculating grinding track of a rotary file with a partitioned circular arc head, which comprises the following steps: firstly, defining structural characteristic parameters and a related coordinate system of a partitioned circular arc head rotary file, and establishing a mathematical model of a peripheral edge line and an end edge line of the partitioned circular arc head rotary file; secondly, defining a reference grinding posture of the grinding wheel; on the basis, a coordinate transformation matrix is adopted to describe the motion mode of the grinding wheel, and the calculation of the grinding position and the posture of the grinding wheel is deduced by means of the principle of kinematics. The method has the characteristics of good structural parameter adaptability, flexible partition adjustment and the like, can obtain the partition type circular arc head rotary file edge line model based on the workpiece coordinate system, and can meet the design and processing requirements of the circular arc head rotary file.
Description
Technical Field
The invention belongs to the technical field of rotary file structure design and grinding manufacturing, and particularly relates to a method for calculating a grinding track of a rotary file with a partitioned circular arc head.
Background
The rotary file is used as a novel cutter, has the characteristics of high production efficiency, good processing quality, long service life and the like [1], and is used for finishing the surfaces of various parts and cleaning burrs and welding seams of weldments; the method can also be used for finishing the processing of the precise die cavity and the complex curved surface of the impeller runner part, and is widely applied to the manufacturing of ships, airplanes, dies and mechanical equipment [2] [3]; the rotary file has the advantages of smaller overall size, various varieties and specifications, smooth and same-direction line type without intersection, multiple teeth and complex edge curves, and the edge curves are spiral lines, so that the difficulty [4] [5] is increased for grinding and manufacturing the rotary file tool. However, since China starts too late in the field of numerical control machine tools, developed countries monopoly large-scale numerical control equipment in China in high-end markets, and core equipment and technology of rotary file processing are not available in China [6]. In addition, the five-axis linkage processing technology is a difficult point, and the quality of the finished product of the rotary file currently produced by domestic manufacturers cannot guarantee and meet the processing requirements of various industries on the rotary file [7]. In the processing and manufacturing of the rotary file tool, the research of blade curve and grinding track planning and multi-axis numerical control processing technology is carried out, and an important theoretical basis is provided for improving the efficiency, cutting performance and processing quality of the rotary file manufacturing and production.
Many students have conducted research work on complex cutter blade line planning including flat head rotary files, arc rotary files, and ball head rotary files. For example, zhou Changxiu et al propose tooth slot forming principle of the cutter and determination of motion function of a grinding system aiming at three different forms of plane curve type, equal helix angle and compound type cutting edge in the aspect of forming principle of the cutting edge of the special rotary surface cutter, so that diversity [8] [9] of the appearance profile of the cutting edge of the rotary surface cutter is realized. Liu Gu the forming theory research of the partitioned special rotary surface cutter [10]; tang Yifeng [11] et al studied the movements of each axis of a numerically controlled machine tool special for screw files, realized smooth transition of cylinder and ball head by interpolation fitting of blade curves, and realized calculation of movement track by coordinate conversion. However, the method has a large calculated amount, and interference or over-cutting is easy to occur in the processing process.
Also, there is a study on the grinding and manufacturing of rotary file to a certain extent, liu Guran [12] [13] simply reforms the tool grinder, and semi-automatic processing of conical and arc rotary file is realized by forming method; zhang Shichang, li Guoqin [14] and the like analyze the geometric model of the ball head rotary file and combine with a four-coordinate machine tool structure to deduce a sharpening motion model under the condition of reducing the swinging of the grinding tool, realize the multi-coordinate linkage control of the machine tool sharpening rotary file, and increase the feasibility of the four-coordinate numerical control sharpening technology of the rotary file.
However, there is little research into the circular arc head partitioned rotary file, and there is less discussion of the related literature on the circular arc head partitioned rotary file method. On the other hand, most developed countries use large numerical control machining equipment, monopoly the cutter market in developed and developing countries, and although there is a certain degree of research in this field in China, there is still a great gap from foreign countries. In order to shorten the gap between the cutter manufacturing capability of China and the cutter manufacturing capability of the industry developed China. The automatic competitiveness of China in the cutter processing industry is improved, so that the development of Chinese cutters is not limited by people, and Chinese cutter enterprises have better living space and are in the state of being in the state of equipment manufacturing industry.
Reference to the literature
[1] Kangjia medical dental rotary file sharpening programming technical research [ D ]. Hubei university, 2018.
[2] Lin Xue, tian Fengjie, li Lun application of rotary files in complex curved surface machining [ J ]. Photovoltaic application, 2019,34 (05): 72-76
[3] Song Qing the automatic programming technical research of multi-axis numerical control processing of partition type rotary file [ D ]. University of science and technology in China, 2014.
[4] Zhao Jun development and research of IPC-based rotary file numerically controlled sharpening System [ D ]. Tianjin university, 2004.
[5] Guo Weijun design and implementation of control system for numerically controlled sharpening machine of rotary file [ D ]. Tianjin university, 2007.
[6] Liu Mingming five-axis numerical control grinding technology research of eccentric staggered tooth type cutter [ D ]. Hunan university, 2018.
[7] Development and research of rotary file numerical control sharpening simulation system based on OpenGL [ D ]. Tianjin university, 2005.
[8] Zhou Changxiu principle of grinding special rotary face cutters with equal helix angle edge [ J ]. University of southeast university, 1992 (01): 8-15
[9] Zhou Changxiu principle of forming tooth grooves of special rotary face cutter of composite blade [ J ]. University of southeast, 1992 (03): 68-74
[10] Liu Guran principle of forming partition (staggered tooth) special rotary surface cutter [ J ]. Mechanical design and manufacture, 1995 (05): 33-36
[11] Tang Yifeng, chen Xinhua, zhou Zhongwang, zhao Junsheng. Numerical control machining method of rotary file with sphere and cylinder combination. Ind. Manufacturing Automation, 2010,32 (08): 188-190.
[12] Liu Guran semi-automatic numerical control processing of a pretty arc rotary file [ J ]. Weapon automation, 2004 (04): 42.
[13] Liu Guran, pretty, two-coordinate processing of conical rotary file [ J ]. Weapon Automation, 2004 (04): 63.
[14] Zhang Shichang, li Guoqin. Study of rotary file four coordinate numerically controlled sharpening technique [ J ]. Tool technique, 2001 (03): 16-18.
Disclosure of Invention
Aiming at the problems that the cutter teeth of a common rotary file are intersected at the top of a cutter, the chip containing space at the top is small, and the cutting condition is poor, the grinding quality of an arc head is improved, and the invention provides a method for calculating the grinding track of a rotary file with a partitioned arc head.
The invention discloses a method for calculating grinding track of a partitioned circular arc head rotary file, which comprises the following steps:
step 1: and defining geometric parameters of the partitioned circular arc head rotary file.
Tool start radius R w The method comprises the steps of carrying out a first treatment on the surface of the I.e. the peripheral tooth is in the form of a helical blade the radius of the cutter at the beginning;
cutter taper angle k: the included angle between the outer contour of the cutter rotation body and the center axis of the cutter rotation body;
length L of peripheral edge w : the length of the peripheral teeth along the axial direction of the cutter;
peripheral edge helix angle beta: is the included angle between the circumferential edge revolution contour generatrix and the circumferential edge line tangent vector;
interdental angle α: rotating central angles clamped by corresponding points of two adjacent blade lines of the file;
depth d of cylindrical initial tooth 1 : defining the depth of a grinding wheel grinding workpiece at the initial position of the cylinder;
end edge circular arc edge initial tooth depth d 2 : defining the depth of a grinding wheel grinding workpiece at the initial position of the arc edge of the end edge;
end edge circular arc edge end point tooth depth d 3 : defining the depth of a grinding wheel grinding workpiece at the end point of the end edge circular arc edge;
depth d of top tooth of cutter 4 : defined as the depth to which the grinding wheel grinds the workpiece at the position of the tool tip.
Step 2: and (5) defining a coordinate system.
WCS (coordinate system) of workpiece
Defining a workpiece coordinate system O W -X W Y W Z W Which takes the axis of the tool as the coordinate axis Z W With origin O W The straight line pointing to the starting point of the spiral blade line is the coordinate axis X W 。
End blade coordinate system DCS
Defining an end edge coordinate system O D -X D Y D Z D Z is wound by the coordinate system of the workpiece W Rotation angle of shaftAnd then along Z W Axial translation L w Obtained.
Step 3: and transforming a coordinate system.
Definition M D→W 、T D→W A rotation matrix and a translation matrix from the end edge coordinate system to the workpiece coordinate system, respectively, then:
in the method, in the process of the invention,
step 4: and carrying out parameterization modeling on the edge line of the rotary file with the partitioned circular arc head, and carrying out parameterization modeling on the edge line divided into a peripheral edge and an end edge part.
S4.1, a partition type circular arc head rotary file peripheral edge line model.
The peripheral edge line on the cylindrical curved surface is established on a workpiece coordinate system O W -X W Y W Z W Lower, in Z W The coordinate value z of the axis is an independent variable, then any point P on the curve 1 The expression of the coordinates is as follows:
representing the edge point P 1 The rotation angle of the starting point of the edge line relative to the workpiece coordinate system is expressed as follows:
wherein the independent variable Z is Z W An axis coordinate value.
S4.2, a partitioned circular arc head rotary file end edge line model.
Firstly, defining the number of end edge partitions of a rotary file tool as m, the number of tool teeth of each partition as n, adopting a mode of intersecting a non-orthogonal spiral rotation surface and an arc rotation surface, and introducing a latitude angle theta as a self-variationMeasuring and establishing the rotation angleThereby obtaining an expression of the circular arc leading edge line, which is described in the end edge coordinate system, respectively.
S4.2.1 curved portion of circular arc rotary surface
The curve part is obtained by intersecting an arc rotary surface with a non-orthogonal spiral surface, the arc cutting edge curve is regarded as a generalized spiral line on the arc rotary surface, and the arc cutting edge line is also regarded as a curve formed by a certain moving point P moving on the arc rotary surface according to a certain rotation rule; any edge point P on the segment curve 0 The coordinates of (c) are expressed as:
wherein, the independent variable theta is an independent variable latitude angle, R is an end edge arc radius, R is an arc center distance, and the expression is as follows:
R＝R w -L w tank-rcosk (7)
representing the arc edge point P 0 At the corner, the corner is +.>The form of (c) is written as a function of the latitude angle theta as a parameter, which will be different depending on the cutting edge of the tool partition>Is expressed in terms of->The expression of (2) can obtain the curve model of the arc rotary surface.
(1) For calculating the turning angle of the edge point on the main edge, the curve of the main edge needs to be communicatedThe center of the top of the over-rotation file is used for obtaining the curve turning angle of the circular arc edge of the main edgeThe expression is as follows:
(2) For calculating the turning angle of the edge point on the auxiliary edge, the curve of the auxiliary edge has an eccentric value, which does not pass through the center of the top of the rotary file tool, and the turning angle of the edge line point also needs to be added with the dividing angle between the edge lines, so that the turning angle of the curve of the auxiliary edge circular arc edgeThe expression is as follows:
in the formula, h represents the eccentric amount of the auxiliary blade line, and n×m represents the total blade tooth number of the rotary file.
S4.2.2 plane curved portion
Curve P 3 P 4 At the passing point P 3 And is in line with the coordinate plane X D O D Y D The curve is established on a plane M perpendicular to the plane M and can be regarded as P 3 The point being in the coordinate plane X D O D Y D Projection point O of (2) r A section of arc which is the center of a circle; due to P 3 The point is the highest point of the arc surface of revolution, so curve P 3 P 4 Section at P 3 Tangent vector F at a point p1 Must lie on plane M and this point lies on a straight bus, which is also on the plane, thus, from curve P 2 P 3 Segment to curve P 3 P 4 The connection of the segments is smooth, so that the segment curves at the edge point P 0 The expression of (2) is:
wherein eta is the inner inclination angle of the circular arc blade, inRepresenting the point P of the edge when θ=pi/2 3 The rotation angle of the position->Representing planes M and X D The included angle of the shaft, which is also referred to above, is expressed as the primary and secondary edges.
(1) The upper plane M of the edge curve of the main edge is the center of the top of the over-rotation file, and the upper planes M and X of the circular arc edge curve of the main edge D The included angle of the axes, namely the highest point P of the arc rotary surface 3 Angle of rotation atNamely:
therefore, the expression of the planar curve of the main edge circular arc curve portion is:
for the auxiliary blade line, due to the eccentric quantity, the plane M does not pass through the center of the top of the rotary file cutter and passes through the point P 3 And is tangential to the cylinder of eccentricity, curve P 3 P 4 Build on the plane; thus, the planar curve expression on the minor edge curve is:
in the method, in the process of the invention,then the upper plane M and X of the arc blade curve of the auxiliary blade D The included angle of the shaft is expressed as follows:
s4.2.3 straight edge portion
The straight edge part is built on the plane M, in order to ensure smooth connection of the straight edge and the arc edge line of the end edge, the straight edge is along the vector direction of the end point of the arc edge, the main edge and the auxiliary edge are also separately described, and the straight edge is defined as a straight line section P on the plane M 4 P 5 The method comprises the steps of carrying out a first treatment on the surface of the It can be seen that the end point P on the end blade plane curve 4 Coordinates of (c):
end edge plane curve end point P 4 Tangent vector F at t1_d The method comprises the following steps:
introducing an independent variable L, the edge point P on the straight edge 0 The expression of (2) is:
wherein L is h The mathematical expressions of the linear edge lengths of the main edge and the auxiliary edge are different for the linear edge lengths of the end edge, and the main edge and the auxiliary edge are described respectively.
(1) For the partition main blade, the blade curve is free from eccentric amount, the plane M of the linear blade passes through the vertex of the circular arc head rotary cutter, and simultaneously passes through the tail point of the circular arc blade plane curve and the center of the end blade coordinate system; the expression of the length of the straight edge of the partitioned main edge is as follows:
(2) For the secondary edge line, the plane M does not pass through the center of the top of the rotary file cutter due to the eccentric amount, the ith secondary edge and the next main edge of the partition are intersected at a point, and the intersection point P 5 And the end point P of the straight edge of the auxiliary edge 4 The space distance of the pair of the straight edges is the length of the straight edge of the pair of the blades; the expression can be deduced from the geometrical relationship as:
L i representing the plane X of the linear edge of the sub-edge of the partition in the end edge coordinate system D O D Y D Projection section P', on 4 P″ 5 Length expressed as:
wherein k is i The main blade straight blade which is intersected with the auxiliary blade is arranged on the end blade coordinate plane X D O D Y D The slope of the upper straight line projection can be obtained by the relative position between the auxiliary blade and the main blade and the indexing relation of the rotating curved surface, and is expressed as:
where m represents the number of rotating file teeth partition groups.
The linear edge length of each sub-edge linear edge can be obtained by calculating the formulas (18), (19), (20) and (21) and simultaneously, and the expression for deriving the sub-edge linear edge length through the geometric relationship is as follows: the complete expression is as follows:
s4.2.4 transformation to the workpiece coordinate System
And (3) converting coordinates of any point on the partitioned blade line of the end blade part into matrixes (1) and (2) through a coordinate system, so that the complete expression of the main blade and each auxiliary blade line in one partition under the coordinate system of the workpiece is obtained, the blade line of the adjacent partition can rotate by 2 pi/m angles after the blade line returns to the initial processing position, and the main blade and the auxiliary blade line of the next partition can be obtained, wherein m is the partition number of the rotary file.
Step 5: the initial attitude of the grinding wheel is defined.
Reference grinding posture of peripheral edge grinding wheel
Defining a reference grinding attitude of the grinding wheel under a coordinate system WCS, and using the center coordinates O of the end face of the grinding wheel g With the grinding wheel axis vector F g Describing the attitude of a grinding wheel; will P 1 The tangent vector at the point is taken as the tangent vector F of the grinding wheel t It is expressed in coordinate system WCS as:
will P 1 Point at point P 1 Plane coordinate Z of point W The vector of the axis is taken as the radial vector F of the grinding wheel b It is expressed in coordinate system WCS as:
grinding wheel shaft vector F g Vector of the tangential direction F t Radial vector F of grinding wheel b Mutually perpendicular, expressed in the coordinate system WCS as:
F g_W ＝F t_W ×F b (benchmark) _W (25)
Reference grinding posture of end edge grinding wheel
The grinding posture of the grinding wheel of the end blade part takes the curve of the arc blade of the end blade as a reference and takes the tangent vector F of the curve t As a tangent vector in the grinding process of the grinding wheel, it is expressed as follows in a coordinate system DCS:
in the method, in the process of the invention,representing the edge line point P 0 Corner of the foot, the head>
With arc center O r P pointing on the curve of the circular-arc edge 2 The vector of points is taken as the radial vector F of the grinding wheel b Arc midpoint O r The coordinates of (c) are expressed as:
radial vector F b Expressed in the coordinate system DCS as:
in the method, in the process of the invention,
grinding wheel shaft vector F g Cutting vector F with grinding wheel t And radial vector F of grinding wheel b Mutually perpendicular, expressed in the coordinate system DCS as:
F g_D ＝F b_D ×F t_D (29)
step 6: and (5) calculating the grinding attitude of the grinding wheel.
(a) Grinding attitude of peripheral edge angle lifting grinding wheel
Defining the lifting angle delta of the grinding wheel as the tangential vector F of the cutting edge point of the grinding wheel with the rotary contour t An angle through which the rotation shaft rotates; let the transformation matrix of rotation angle epsilon around any unit vector N of space be Rot (N, epsilon), then it is expressed as:
wherein vers (ε) =1-cos ε, i N 、j N 、k N Respectively, the components in three directions of the vector N, and epsilon represents the rotation angle.
Radial vector F of peripheral edge portion after the grinding wheel is introduced with lift angle delta b With the grinding wheel axis vector F g Respectively converted into F' b And F' g Radial vector F b It is expressed in WCS coordinate system as:
grinding wheel shaft vector F g Expressed in coordinate system WCS as:
F' g_W ＝F t_W ×F b ′ _W (32)
(b) Grinding attitude of end edge angle lifting grinding wheel
Similarly, the grinding wheel lifting angle delta is also introduced under the grinding posture of the end blade grinding wheel, and after the grinding wheel lifting angle delta is introduced, the radial vector F of the end blade part b With the grinding wheel axis vector F g Conversion to F' b And F' g It is expressed in DCS coordinate system as:
F′ b_D ＝Rot(F t_D ,δ)F b_D (33)
F' g_D ＝F′ b_D ×F t_D (34)
grinding wheel axis vector F' g This can be calculated from the following formula:
F' g_D ＝F' b_D ×F t_D (35)
step 7: calculating grinding track of a grinding wheel;
(1) Computing grinding track of peripheral edge grinding wheel
According to the definition of the grinding posture, based on the description of a workpiece coordinate system, the center point O of the end face of the grinding wheel g Is to coordinate description of sandThe constraint condition of the grinding position of the wheel is that the large end face of the grinding wheel is always contacted with the edge line in the grinding process; can be obtained at the center point O of the grinding wheel end circle g The coordinates in the peripheral edge coordinate system are expressed as:
O′ g1 _ W ＝P P1_W +(R g -d 13 )F b ′_ W (36)
wherein R is g Is the circumference radius of the large end face of the grinding wheel, d 12 Grinding depth for peripheral edge part of rotary file and tooth depth d of peripheral edge part 1 And end edge circular arc edge initial tooth depth d 2 Keeping consistent, the expression is:
wherein k is s The angle of taper of the grinding wheel is denoted, gamma denotes the rake angle, and m x n denotes the total number of teeth of the rotary rasp.
(2) End edge grinding wheel grinding track calculation
Describing the grinding track of the end blade part grinding wheel, defining the grinding center point O of the grinding wheel of the grinding track of the end blade according to the end blade line and the grinding posture of the end blade grinding wheel g The coordinates in the end-edge coordinate system are expressed as:
O g0 _ D ＝P P ′ 0_D +(R g -d 24 )F b ″_ D (38)
wherein R is g Is the circumference radius of the large end face of the grinding wheel, d 24 For rotating the end edge part grinding depth of the file, wherein the end edge circular arc edge starts to be deep d 2 And arc edge end point tooth depth d 3 Is equal, so the grinding depth of the end blade portion is expressed as:
the beneficial technical effects of the invention are as follows:
the method has the characteristics of good structural parameter adaptability, flexible partition adjustment and the like, and can obtain the partition type circular arc head rotary file edge line model based on the workpiece coordinate system. Can meet the design and processing requirements of the circular arc head rotary file.
Drawings
FIG. 1 is a schematic diagram of parameters of a circular arc head rotary file.
Fig. 2 is a schematic diagram of a coordinate system.
FIG. 3 is a schematic cross-sectional view of a partitioned arcuate head rotary file end.
Fig. 4 is a schematic diagram of modeling of the peripheral edge line.
Fig. 5 is a schematic modeling diagram of a curved portion of the end edge arc surface of revolution.
FIG. 6 is a schematic modeling diagram of a major edge planar curve portion.
FIG. 7 is a schematic modeling of the minor edge planar curve portion.
Fig. 8 is a schematic diagram of a main edge linear edge portion modeling.
Fig. 9 is a schematic diagram of a secondary edge linear edge portion modeling.
Fig. 10 is a view showing the reference grinding posture of the peripheral edge of the circular arc rotary file.
Fig. 11 is a schematic view of the reference grinding profile of the end edge of the circular arc rotary file.
Fig. 12 is a schematic view of the grinding attitude of the peripheral edge grinding wheel after the grinding wheel is added with the lifting angle.
Fig. 13 is a schematic view of the grinding attitude of the end blade grinding wheel after the grinding wheel is added with the lifting angle.
Fig. 14 is a simulation drawing of the verify grinding of the partitioned circular arc head rotary file.
Fig. 15 is a view of actual machining and tool measurement.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
The invention discloses a method for calculating grinding track of a partitioned circular arc head rotary file, which comprises the following steps:
step 1: and defining geometric parameters of the partitioned circular arc head rotary file.
For a more complete and accurate analysis and study of the structure of a circular arc head rotating file, as shown in fig. 1, the following parameters are defined:
cutter liftInitial radius of gyration R w The method comprises the steps of carrying out a first treatment on the surface of the I.e. the radius of the cutter of the peripheral tooth spiral edge at the beginning;
cutter taper angle k: the included angle between the outer contour of the cutter rotation body and the center axis of the cutter rotation body;
length L of peripheral edge w : the length of the peripheral teeth along the axial direction of the cutter;
taper angle κ: an included angle between a circumferential tooth rotation contour generatrix and the axis of the cutter;
peripheral edge helix angle beta: is the included angle between the circumferential edge revolution contour generatrix and the circumferential edge line tangent vector;
interdental angle α: rotating central angles clamped by corresponding points of two adjacent blade lines of the file;
depth d of cylindrical initial tooth 1 : defining the depth of a grinding wheel grinding workpiece at the initial position of the cylinder;
end edge circular arc edge initial tooth depth d 2 : defining the depth of a grinding wheel grinding workpiece at the initial position of the arc edge of the end edge;
end edge circular arc edge end point tooth depth d 3 : defining the depth of a grinding wheel grinding workpiece at the end point of the end edge circular arc edge;
depth d of top tooth of cutter 4 : defined as the depth to which the grinding wheel grinds the workpiece at the position of the tool tip.
Step 2: the coordinate system is defined (as shown in fig. 2).
WCS (coordinate system) of workpiece
Defining a workpiece coordinate system O W -X W Y W Z W Which takes the axis of the tool as the coordinate axis Z W With origin O W The straight line pointing to the starting point of the spiral blade line is the coordinate axis X W . The tool position coordinates of the grinding track of the grinding wheel finally need to be described in a workpiece coordinate system.
End blade coordinate system DCS
Defining an end edge coordinate system O D -X D Y D Z D Z is wound by the coordinate system of the workpiece W Rotation angle of shaftAnd then along Z W Axial translation L w Obtained.
Step 3: and transforming a coordinate system.
In order to facilitate the post-processing of the grinding wheel tool setting and the numerical control grinding machine, the following coordinate system transformation matrix is constructed: definition M D→W 、T D→W A rotation matrix and a translation matrix from the end edge coordinate system to the workpiece coordinate system, respectively, then:
in the method, in the process of the invention,
step 4: and (5) parameterizing and modeling the rotary file edge line of the partitioned circular arc head.
In the design method of the partition type circular arc head rotary file edge line, as shown in fig. 3, the edges are divided into two types, one type is that the edges converged at the center of the top of the cutter are defined as main edges, the other type is that the edges not converged at the center of the top of the cutter are defined as auxiliary edges, the edges are arranged in such a way, the chip containing space among the edges is increased, and the improvement of cutting conditions can be realized. The arc-shaped cutting edge curve of the rotary file with the partitioned arc head is divided into an equal spiral cutting edge line of a cylindrical peripheral cutting edge and an arc-shaped cutting edge curve of an end cutting edge part, so that smoothness of the cutting edge curve is guaranteed, cutting machining is facilitated, the arc-shaped cutting edge curve and the peripheral cutting edge line are smoothly transited, and the generalized spiral angles of the arc-shaped cutting edge line and the peripheral cutting edge at the joint are required to be the same. The edge line is parameterized and modeled to divide the peripheral edge and the end edge portions.
S4.1, a partition type circular arc head rotary file peripheral edge line model.
In the cylindrical part of the rotary file, the peripheral edge line is designed into an equal helix angle curve, namely the spiral movement direction and the contourThe generatrix has a constant included angle in order to ensure that the flow direction of the swarf of the rotary file remains consistent during the grinding process. The study of the peripheral edge line is described in many documents. The peripheral edge line on the cylindrical curved surface is established in a workpiece coordinate system O W -X W Y W Z W Next, as shown in FIG. 4, Z is W The coordinate value z of the axis is an independent variable, then any point P on the curve 1 The expression of the coordinates is as follows:
representing the edge point P 1 The rotation angle of the starting point of the edge line relative to the workpiece coordinate system is expressed as follows:
wherein the independent variable Z is Z W An axis coordinate value.
S4.2, a partitioned circular arc head rotary file end edge line model.
When describing the partitioned circular arc head end edge line model, the number of end edge partitions of the rotary file tool is defined as m, and the number of tool teeth of each partition is defined as n. The end edge curve is divided into a main edge and a secondary edge according to the difference of the cutting action, and in order to accurately and clearly describe the arc edge curve, modeling of the end edge arc edge line part is performed in a spiral revolution surface mode by referring to a ball end edge line construction mode of Cheng and the like. By adopting a mode of solving intersection line of a non-orthogonal spiral rotation surface and an arc rotation surface and introducing a latitude angle theta as an independent variable, the intersection line and the rotation angle are establishedThereby obtaining an expression of the circular arc leading edge line, which is described in the end edge coordinate system, respectively.
S4.2.1 curved portion of circular arc rotary surface
The curve part is obtained by intersecting a circular arc rotary surface and a non-orthogonal spiral surface, the circular arc cutting edge curve is regarded as a generalized spiral line on the circular arc rotary surface, the circular arc cutting edge line is also regarded as a curve formed by a certain moving point P moving on the circular arc rotary surface according to a certain rotation rule, as shown in figure 5, any cutting edge point P on the curve 0 The coordinates of (c) are expressed as:
wherein, the independent variable theta is an independent variable latitude angle, R is an end edge arc radius, R is an arc center distance, and the expression is as follows:
R＝R w -L w tank-rcosk (7)
representing circular arc edges blade point P 0 At the corner, the corner is +.>The form of (c) is written as a function of the latitude angle theta as a parameter, which will be different depending on the cutting edge of the tool partition>Is expressed in terms of->The expression of (2) can obtain the curve model of the arc rotary surface.
(1) For calculating the turning angle of the cutting edge point on the main cutting edge, the turning angle of the circular arc cutting edge curve of the main cutting edge is obtained by rotating the center of the top of the file cutter according to the cutting edge curve of the main cutting edgeThe expression is as follows:
(2) For calculating the turning angle of the edge point on the auxiliary edge, the curve of the auxiliary edge has an eccentric value, which does not pass through the center of the top of the rotary file tool, and the turning angle of the edge line point also needs to be added with the dividing angle between the edge lines, so that the turning angle of the curve of the auxiliary edge circular arc edgeThe expression is as follows:
in the formula, h represents the eccentric amount of the auxiliary blade line, and n×m represents the total blade tooth number of the rotary file.
S4.2.2 plane curved portion
Curve P 3 P 4 At the passing point P 3 And is in line with the coordinate plane X D O D Y D The curve is established on a plane M perpendicular to the plane M and can be regarded as P 3 The point being in the coordinate plane X D O D Y D Projection point O of (2) r A section of arc which is the center of a circle; due to P 3 The point is the highest point of the arc surface of revolution, so curve P 3 P 4 Section at P 3 Tangent vector F at a point p1 Must lie on plane M and this point lies on a straight bus, which is also on the plane, thus, from curve P 2 P 3 Segment to curve P 3 P 4 The connection of the segments is smooth, so that the segment curves at the edge point P 0 The expression of (2) is:
wherein eta is the inner inclination angle of the circular arc blade, inWhen θ=pi/2 is expressed, i.eBlade point P 3 The rotation angle of the position->Representing planes M and X D The included angle of the shaft, which is also referred to above, is expressed as the primary and secondary edges.
(1) The plane M on the edge curve of the main edge is the center of the top of the over-rotated rasp, as shown in fig. 6. Main edge circular arc edge upper plane M and X D The included angle of the axes, namely the highest point P of the arc rotary surface 3 Angle of rotation atNamely:
therefore, the expression of the planar curve of the main edge circular arc curve portion is:
for the minor edge line, the plane M does not pass through the center of the top of the rotating file due to its eccentricity, as shown in fig. 7. Plane M passing point P 3 And is tangential to the cylinder of eccentricity, curve P 3 P 4 Build on the plane; thus, the planar curve expression on the minor edge curve is:
in the method, in the process of the invention,then the upper plane M and X of the arc blade curve of the auxiliary blade D The included angle of the shaft is expressed as follows:
s4.2.3 straight edge portion
The straight edge part is built on the plane M, in order to ensure smooth connection of the straight edge and the arc edge line of the end edge, the straight edge is along the vector direction of the end point of the arc edge, the main edge and the auxiliary edge are also separately described, and the straight edge is defined as a straight line section P on the plane M 4 P 5 The method comprises the steps of carrying out a first treatment on the surface of the It can be seen that the end point P on the end blade plane curve 4 Coordinates of (c):
end edge plane curve end point P 4 Tangent vector F at t1_d The method comprises the following steps:
introducing an independent variable L, the edge point P on the straight edge 0 The expression of (2) is:
wherein L is h The mathematical expressions of the linear edge lengths of the main edge and the auxiliary edge are different for the linear edge lengths of the end edge, and the main edge and the auxiliary edge are described respectively.
(1) For the partition main blade, the blade curve is free from eccentric amount, the plane M of the linear blade passes through the vertex of the circular arc head rotary cutter, and simultaneously passes through the tail point of the circular arc blade plane curve and the center of the end blade coordinate system; as shown in fig. 8. The expression of the length of the straight edge of the partitioned main edge is as follows:
(2) For the auxiliary edge line, the eccentric amount existsThe plane M does not pass through the center of the top of the rotary file tool, the ith auxiliary blade and the next main blade of the partition are intersected at a point, and the intersection point P 5 And the end point P of the straight edge of the auxiliary edge 4 The space distance of the pair of the straight edges is the length of the straight edge of the pair of the blades; as shown in fig. 9. The expression can be deduced from the geometrical relationship as:
L i representing the plane X of the linear edge of the sub-edge of the partition in the end edge coordinate system D O D Y D Projection section P', on 4 P″ 5 Length expressed as:
wherein k is i The main blade straight blade which is intersected with the auxiliary blade is arranged on the end blade coordinate plane X D O D Y D The slope of the upper straight line projection can be obtained by the relative position between the auxiliary blade and the main blade and the indexing relation of the rotating curved surface, and is expressed as:
wherein m represents the number of the rotating file tooth partition groups;
the linear edge length of each sub-edge linear edge can be obtained by calculating the formulas (18), (19), (20) and (21) and simultaneously, and the expression for deriving the sub-edge linear edge length through the geometric relationship is as follows: the complete expression is as follows:
s4.2.4 transformation to the workpiece coordinate System
Since the edge lines need to be described in a uniform coordinate system, the edge line expression calculated in the end edge coordinate system needs to be transformed into the workpiece coordinate system. And (3) converting coordinates of any point on the partitioned blade line of the end blade part into matrixes (1) and (2) through a coordinate system, so that the complete expression of the main blade and each auxiliary blade line in one partition under the coordinate system of the workpiece is obtained, the blade line of the adjacent partition can rotate by 2 pi/m angles after the blade line returns to the initial processing position, and the main blade and the auxiliary blade line of the next partition can be obtained, wherein m is the partition number of the rotary file.
Step 5: the initial attitude of the grinding wheel is defined.
Reference grinding posture of peripheral edge grinding wheel
The grinding attitude of the grinding wheel of the circular arc head rotary file peripheral edge adopted by the invention is shown in figure 10, the reference grinding attitude of the grinding wheel is defined under the coordinate system WCS, the grinding wheel adopted by the grinding is a conical grinding wheel for conveniently converting the grinding wheel attitude into a numerical control program, the precise processing of a rake angle can be realized for a given grinding wheel, and the regulation of the rake angle can be met and the design requirement of the groove depth can be met by reasonably selecting the cone base angle of the grinding wheel. With the center coordinates O of the end face of the grinding wheel g With the grinding wheel axis vector F g Describing the attitude of a grinding wheel; will P 1 The tangent vector at the point is taken as the tangent vector F of the grinding wheel t It is expressed in coordinate system WCS as:
will P 1 Point at point P 1 Plane coordinate Z of point W The vector of the axis is taken as the radial vector F of the grinding wheel b It is expressed in coordinate system WCS as:
grinding wheel shaft vector F g Vector of the tangential direction F t Radial vector F of grinding wheel b Mutually perpendicular, expressed in the coordinate system WCS as:
F g_W ＝F t_W ×F b (benchmark) _W (25)
Reference grinding posture of end edge grinding wheel
The grinding attitude of the grinding wheel of the end blade part adopted for the invention is shown in fig. 11, and the cutting vector F of the curve is based on the curve of the arc edge of the end blade t As a tangent vector in the grinding process of the grinding wheel, it is expressed as follows in a coordinate system DCS:
in the method, in the process of the invention,representing the edge line point P 0 Corner of the foot, the head>
With arc center O r P pointing on the curve of the circular-arc edge 2 The vector of points is taken as the radial vector F of the grinding wheel b Arc midpoint O r The coordinates of (c) are expressed as:
radial vector F b Expressed in the coordinate system DCS as:
in the method, in the process of the invention,
grinding wheel shaft vector F g Cutting vector F with grinding wheel t And radial vector F of grinding wheel b Mutually perpendicular, expressed in the coordinate system DCS as:
F g_D ＝F b_D ×F t_D (29)
step 6: and (5) calculating the grinding attitude of the grinding wheel.
(a) Grinding attitude of peripheral edge angle lifting grinding wheel
In order to avoid the interference problem between the teeth of the rotary file in the actual grinding process, the lifting angle of the grinding wheel is defined as the tangential vector F of the grinding wheel by the rotary contour blade point t A lift angle delta for the rotation shaft to rotate; as shown in fig. 12. Let the transformation matrix of rotation angle epsilon around any unit vector N of space be Rot (N, epsilon), then it is expressed as:
wherein vers (ε) =1-cos ε, i N 、j N 、k N Respectively, the components in three directions of the vector N, and epsilon represents the rotation angle.
Radial vector F of peripheral edge portion after the grinding wheel is introduced with lift angle delta b With the grinding wheel axis vector F g Respectively converted into F' b And F' g Radial vector F b It is expressed in WCS coordinate system as:
F′ b_W ＝Rot(F t_W ,δ)F b (benchmark) _W (31)
Grinding wheel shaft vector F g Expressed in coordinate system WCS as:
F' g_W ＝F t_W ×F′ b_W (32)
(b) Grinding attitude of end edge angle lifting grinding wheel
Similarly, the grinding wheel lift angle delta is also introduced in the end blade grinding attitude, as shown in fig. 13. After introduction of the grinding wheel lift angle delta, the radial vector F of the end blade portion b With the grinding wheel axis vector F g Conversion to F' b And F' g It is expressed in DCS coordinate system as:
F′ b_D ＝Rot(F t_D ,δ)F b_D (33)
F' g_D ＝F′ b_D ×F t_D (34)
grinding wheel axis vector F' g This can be calculated from the following formula:
F' g_D ＝F' b_D ×F t_D (35)
step 7: calculating grinding track of a grinding wheel;
(1) Computing grinding track of peripheral edge grinding wheel
According to the definition of the grinding posture, based on the description of a workpiece coordinate system, the center point O of the end face of the grinding wheel g The grinding position of the grinding wheel is described by the coordinates of the grinding wheel, and the constraint condition is that the large end face of the grinding wheel is always contacted with the edge line in the grinding process; can be obtained at the center point O of the grinding wheel end circle g The coordinates in the peripheral edge coordinate system are expressed as:
O′ g1_W ＝P P1_W +(R g -d 13 )F′ b_W (36)
wherein R is g Is the circumference radius of the large end face of the grinding wheel, d 12 Grinding depth for peripheral edge part of rotary file and tooth depth d of peripheral edge part 1 And end edge circular arc edge initial tooth depth d 2 Keeping consistent, the expression is:
wherein k is s The angle of taper of the grinding wheel is denoted, gamma denotes the rake angle, and m x n denotes the total number of teeth of the rotary rasp.
(2) End edge grinding wheel grinding track calculation
Describing the grinding track of the end blade part grinding wheel, defining the grinding center point O of the grinding wheel of the grinding track of the end blade according to the end blade line and the grinding posture of the end blade grinding wheel g The coordinates in the end-edge coordinate system are expressed as:
O g0 _ D ＝P′ P0_D +(R g -d 24 )F″ b_D (38)
wherein R is g Is the circumference radius of the large end face of the grinding wheel, d 24 For rotating the end edge part grinding depth of the file, wherein the end edge circular arc edge starts to be deep d 2 And arc edge end point tooth depth d 3 Is equal, so the grinding depth of the end blade portion is expressed as:
simulation verification:
in order to verify the grinding wheel grinding track algorithm, an algorithm prototype is developed by utilizing a VC++ environment, relevant structural design parameters are input, a tool position track file is output according to the proposed grinding wheel grinding track algorithm, three-dimensional grinding simulation is carried out in a VERICUT8.0, the structural design parameters used for verification are shown in a table 1, and the technological parameters are shown in a table 2.
Table 1 structural design parameters of circular arc head rotating file
Table 2 grinding process parameters of partitioned circular arc head rotary file
The grinding track of the partial grinding wheel of the partitioned circular arc head rotary file is shown in table 3; the simulation results are shown in fig. 14. And then adopting a certain G500T+ type five-axis numerical control tool grinder to carry out actual grinding processing. The actual processing results are shown in fig. 15.
TABLE 3 measurement of parameters for partitioned circular arc head rotary file
As can be seen from the comparative analysis of the results in the table 3 and the table 1, the measured values after the simulation processing of the geometric parameters of the circular arc head rotary file are basically consistent with the design values, which shows that the grinding track algorithm of the circular arc head rotary file provided by the invention can meet the design and processing requirements of the circular arc head rotary file. In actual processing, the abrasion of the arc radius of the grinding wheel may cause a small error in part of parameters actually ground, and a compensation mode can be used to improve the processing precision.
Claims (1)
1. The method for calculating the grinding track of the partitioned circular arc head rotary file is characterized by comprising the following steps of:
step 1: defining geometric parameters of the partitioned circular arc head rotary file:
tool start radius R w The method comprises the steps of carrying out a first treatment on the surface of the I.e. the radius of the cutter of the peripheral tooth spiral edge at the beginning;
cutter taper angle k: the included angle between the outer contour of the cutter rotation body and the center axis of the cutter rotation body;
length L of peripheral edge w : the length of the peripheral teeth along the axial direction of the cutter;
peripheral edge helix angle beta: is the included angle between the circumferential edge revolution contour generatrix and the circumferential edge line tangent vector;
interdental angle α: rotating central angles clamped by corresponding points of two adjacent blade lines of the file;
depth d of cylindrical initial tooth 1 : defining the depth of a grinding wheel grinding workpiece at the initial position of the cylinder;
end edge circular arc edge initial tooth depth d 2 : defining the depth of a grinding wheel grinding workpiece at the initial position of the arc edge of the end edge;
end edge circular arc edge end point tooth depth d 3 : defining the depth of a grinding wheel grinding workpiece at the end point of the end edge circular arc edge;
depth d of top tooth of cutter 4 : defining the depth of a grinding wheel grinding a workpiece at the top end position of the cutter;
step 2: defining a coordinate system;
WCS (coordinate system) of workpiece
Defining a workpiece coordinate system O W -X W Y W Z W Which takes the axis of the tool as the coordinate axis Z W With origin O W The straight line pointing to the starting point of the spiral blade line is the coordinate axis X W ；
End blade coordinate system DCS
Defining an end edge coordinate system O D -X D Y D Z D Z is wound by the coordinate system of the workpiece W Rotation angle of shaftAnd then along Z W Axial translation L w Obtaining;
step 3: transforming a coordinate system;
definition M D→W 、T D→W A rotation matrix and a translation matrix from the end edge coordinate system to the workpiece coordinate system, respectively, then:
in the method, in the process of the invention,
step 4: carrying out parameterization modeling on the edge line of the rotary file of the partitioned circular arc head, and carrying out parameterization modeling on the edge line divided into a peripheral edge and an end edge part;
s4.1, a regional arc head rotary file peripheral edge line model;
the peripheral edge line on the cylindrical curved surface is established on a workpiece coordinate system O W -X W Y W Z W Lower, in Z W The coordinate value z of the axis is an independent variable, then any point P on the curve 1 The expression of the coordinates is as follows:
representing the edge point P 1 The rotation angle of the starting point of the edge line relative to the workpiece coordinate system is expressed as follows:
wherein the independent variable Z is Z W An axis coordinate value;
s4.2, a rotary file end edge line model of the partitioned circular arc head;
firstly, defining the number of end edge partitions of a rotary file tool as m, setting the number of tool teeth of each partition as n, adopting a mode of intersecting a non-orthogonal spiral rotation surface with an arc rotation surface, and establishing a rotation angle and a latitude angle theta by introducing the latitude angle theta as an independent variableThereby obtaining the expression of the arc head edge line, which is respectively described under the end edge coordinate system;
s4.2.1 curved portion of circular arc rotary surface
The curve part is obtained by intersecting an arc rotary surface with a non-orthogonal spiral surface, the arc cutting edge curve is regarded as a generalized spiral line on the arc rotary surface, and the arc cutting edge line is also regarded as a curve formed by a certain moving point P moving on the arc rotary surface according to a certain rotation rule; any edge point P on the segment curve 0 The coordinates of (c) are expressed as:
wherein, the independent variable theta is an independent variable latitude angle, R is an end edge arc radius, R is an arc center distance, and the expression is as follows:
R＝R w -L w tank-rcosk (7)
representing the arc edge point P 0 At the corner, the corner is +.>Is written in the form ofThe function with latitude angle theta as parameter can generate different +.>Is expressed in terms of->The expression of (2) can obtain a curve model of the arc rotary surface;
(1) For calculating the turning angle of the cutting edge point on the main cutting edge, the turning angle of the circular arc cutting edge curve of the main cutting edge is obtained by rotating the center of the top of the file cutter according to the cutting edge curve of the main cutting edgeThe expression is as follows:
(2) For calculating the turning angle of the edge point on the auxiliary edge, the curve of the auxiliary edge has an eccentric value, which does not pass through the center of the top of the rotary file tool, and the turning angle of the edge line point also needs to be added with the dividing angle between the edge lines, so that the turning angle of the curve of the auxiliary edge circular arc edgeThe expression is as follows:
wherein h represents the eccentric amount of the auxiliary blade line, and n×m represents the total blade tooth number of the rotary file;
s4.2.2 plane curved portion
Curve P 3 P 4 At the passing point P 3 And is in line with the coordinate plane X D O D Y D The curve is established on a plane M perpendicular to the plane M and can be regarded as P 3 Point at coordinate levelPlane X D O D Y D Projection point O of (2) r A section of arc which is the center of a circle; due to P 3 The point is the highest point of the arc surface of revolution, so curve P 3 P 4 Section at P 3 Tangent vector F at a point p1 Must lie on plane M and this point lies on a straight bus, which is also on the plane, thus, from curve P 2 P 3 Segment to curve P 3 P 4 The connection of the segments is smooth, so that the segment curves at the edge point P 0 The expression of (2) is:
wherein eta is the inner inclination angle of the circular arc blade, inRepresenting the point P of the edge when θ=pi/2 3 The rotation angle of the position->Representing planes M and X D The included angle of the shaft, which is also divided into the expression of the main blade and the auxiliary blade;
(1) The upper plane M of the edge curve of the main edge is the center of the top of the over-rotation file, and the upper planes M and X of the circular arc edge curve of the main edge D The included angle of the axes, namely the highest point P of the arc rotary surface 3 Angle of rotation atNamely:
therefore, the expression of the planar curve of the main edge circular arc curve portion is:
for the auxiliary blade line, due to the eccentric quantity, the plane M does not pass through the center of the top of the rotary file cutter and passes through the point P 3 And is tangential to the cylinder of eccentricity, curve P 3 P 4 Build on the plane; thus, the planar curve expression on the minor edge curve is:
in the method, in the process of the invention,then the upper plane M and X of the arc blade curve of the auxiliary blade D The included angle of the shaft is expressed as follows:
s4.2.3 straight edge portion
The straight edge part is built on the plane M, in order to ensure smooth connection of the straight edge and the arc edge line of the end edge, the straight edge is along the vector direction of the end point of the arc edge, the main edge and the auxiliary edge are also separately described, and the straight edge is defined as a straight line section P on the plane M 4 P 5 The method comprises the steps of carrying out a first treatment on the surface of the It can be seen that the end point P on the end blade plane curve 4 Coordinates of (c):
end edge plane curve end point P 4 Tangent vector F at t1_D The method comprises the following steps:
introducing an independent variable L, then the straight edgeUpper blade point P 0 The expression of (2) is:
wherein L is h The mathematical expressions of the linear edge lengths of the main edge and the auxiliary edge are different, and the main edge and the auxiliary edge are respectively described;
(1) For the partition main blade, the blade curve is free from eccentric amount, the plane M of the linear blade passes through the vertex of the circular arc head rotary cutter, and simultaneously passes through the tail point of the circular arc blade plane curve and the center of the end blade coordinate system; the expression of the length of the straight edge of the partitioned main edge is as follows:
(2) For the secondary edge line, the plane M does not pass through the center of the top of the rotary file cutter due to the eccentric amount, the ith secondary edge and the next main edge of the partition are intersected at a point, and the intersection point P 5 And the end point P of the straight edge of the auxiliary edge 4 The space distance of the pair of the straight edges is the length of the straight edge of the pair of the blades; the expression can be deduced from the geometrical relationship as:
L i representing the plane X of the linear edge of the sub-edge of the partition in the end edge coordinate system D O D Y D Projection section P', on 4 P″ 5 Length expressed as:
wherein k is i The main blade straight blade which is intersected with the auxiliary blade is arranged on the end blade coordinate plane X D O D Y D The slope of the upper straight line projection can be obtained by the relative position between the auxiliary blade and the main blade and the indexing relation of the rotating curved surface, and is expressed as:
wherein m represents the number of the rotating file tooth partition groups;
the linear edge length of each sub-edge linear edge can be obtained by calculating the formulas (18), (19), (20) and (21) and simultaneously, and the expression for deriving the sub-edge linear edge length through the geometric relationship is as follows: the complete expression is as follows:
s4.2.4 transformation to the workpiece coordinate System
The coordinates of any point on the partitioned blade line of the end blade part are converted into matrixes (1) and (2) through a coordinate system, so that the complete expression of the main blade and each auxiliary blade line in one partition under the coordinate system of the workpiece is obtained, the blade line of the adjacent partition can rotate by 2 pi/m angles after the blade line returns to the initial processing position, and the main blade and the auxiliary blade line of the next partition can be obtained, wherein m is the partition number of the rotary file;
step 5: defining the initial attitude of the grinding wheel;
reference grinding posture of peripheral edge grinding wheel
Defining a reference grinding attitude of the grinding wheel under a coordinate system WCS, and using the center coordinates O of the end face of the grinding wheel g With the grinding wheel axis vector F g Describing the attitude of a grinding wheel; will P 1 The tangent vector at the point is taken as the tangent vector F of the grinding wheel t It is expressed in coordinate system WCS as:
will P 1 Point at point P 1 The point is locatedPlane coordinate Z W The vector of the axis is taken as the radial vector F of the grinding wheel b It is expressed in coordinate system WCS as:
grinding wheel shaft vector F g Vector of the tangential direction F t Radial vector F of grinding wheel b Mutually perpendicular, expressed in the coordinate system WCS as:
F g_W ＝F t_W ×F b (benchmark) _W (25)
Reference grinding posture of end edge grinding wheel
The grinding posture of the grinding wheel of the end blade part takes the curve of the arc blade of the end blade as a reference and takes the tangent vector F of the curve t As a tangent vector in the grinding process of the grinding wheel, it is expressed as follows in a coordinate system DCS:
in the method, in the process of the invention,representing the edge line point P 0 Corner of the foot, the head>
With arc center O r P pointing on the curve of the circular-arc edge 2 The vector of points is taken as the radial vector F of the grinding wheel b Arc midpoint O r The coordinates of (c) are expressed as:
radial vector F b Expressed in the coordinate system DCS as:
in the method, in the process of the invention,
grinding wheel shaft vector F g Cutting vector F with grinding wheel t And radial vector F of grinding wheel b Mutually perpendicular, expressed in the coordinate system DCS as:
F g_D ＝F b_D ×F t_D (29)
step 6: calculating the grinding attitude of the grinding wheel;
(a) Grinding attitude of peripheral edge angle lifting grinding wheel
Defining the lifting angle delta of the grinding wheel as the tangential vector F of the cutting edge point of the grinding wheel with the rotary contour t An angle through which the rotation shaft rotates; let the transformation matrix rotated by an angle α around any unit vector N in space be Rot (N, epsilon), it is expressed as:
wherein vers (ε) =1-cos ε, i N 、j N 、k N Respectively representing components in three directions of a vector N, and epsilon represents a rotation angle;
after the grinding wheel lift angle delta is introduced, the radial vector F of the peripheral edge part b With the grinding wheel axis vector F g Respectively converted into F' b And F' g Radial vector F b It is expressed in WCS coordinate system as:
F′ b_W ＝Rot(F t_W ,δ)F b (benchmark) _W (31)
Grinding wheel shaft vector F g Expressed in coordinate system WCS as:
F' g_W ＝F t_W ×F′ b_W (32)
(b) Grinding attitude of end edge angle lifting grinding wheel
Similarly, the grinding wheel lifting angle delta is also introduced under the grinding posture of the end edge grinding wheel, and the grinding wheel lifting angle delta is formed byAfter the grinding wheel lift angle delta is introduced, the radial vector F of the end blade part b With the grinding wheel axis vector F g Conversion to F' b And F' g It is expressed in DCS coordinate system as:
F′ b_D ＝Rot(F t_D ,δ)F b_D (33)
F' g_D ＝F′ b_D ×F t_D (34)
grinding wheel axis vector F' g This can be calculated from the following formula:
F' g_D ＝F' b_D ×F t_D (35)
step 7: calculating grinding track of a grinding wheel;
(1) Computing grinding track of peripheral edge grinding wheel
According to the definition of the grinding posture, based on the description of a workpiece coordinate system, the center point O of the end face of the grinding wheel g The grinding position of the grinding wheel is described by the coordinates of the grinding wheel, and the constraint condition is that the large end face of the grinding wheel is always contacted with the edge line in the grinding process; can be obtained at the center point O of the grinding wheel end circle g The coordinates in the peripheral edge coordinate system are expressed as:
O′ g1_W ＝P P1_W +(R g -d 13 )F′ b_W (36)
wherein R is g Is the circumference radius of the large end face of the grinding wheel, d 12 Grinding depth for peripheral edge part of rotary file and tooth depth d of peripheral edge part 1 And end edge circular arc edge initial tooth depth d 2 Keeping consistent, the expression is:
wherein k is s The taper angle of the grinding wheel is represented, gamma represents a rake angle, and m multiplied by n represents the total number of teeth of the rotary file;
(2) End edge grinding wheel grinding track calculation
Describing the grinding track of the end blade part grinding wheel, defining the grinding center point O of the grinding wheel of the grinding track of the end blade according to the end blade line and the grinding posture of the end blade grinding wheel g Coordinate table in end blade coordinate systemThe method comprises the following steps:
O g0_D ＝P′ P0_D +(R g -d 24 )F″ b_D (38)
wherein R is g Is the circumference radius of the large end face of the grinding wheel, d 24 For rotating the end edge part grinding depth of the file, wherein the end edge circular arc edge starts to be deep d 2 And arc edge end point tooth depth d 3 Is equal, so the grinding depth of the end blade portion is expressed as:
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| CN116663204B (en) * | 2023-07-31 | 2023-10-17 | 南京航空航天大学 | Offline programming method, system and equipment for robot milling |
| CN118650503A (en) * | 2024-07-19 | 2024-09-17 | 深圳数马电子技术有限公司 | Step surface grinding method, device, CNC machine and storage medium for tool |
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