CN114880786A - Four-axis grinding path generation method for peripheral edge of ball-end mill - Google Patents
Four-axis grinding path generation method for peripheral edge of ball-end mill Download PDFInfo
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- CN114880786A CN114880786A CN202111191683.XA CN202111191683A CN114880786A CN 114880786 A CN114880786 A CN 114880786A CN 202111191683 A CN202111191683 A CN 202111191683A CN 114880786 A CN114880786 A CN 114880786A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06F30/17—Mechanical parametric or variational design
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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
- B24B3/02—Sharpening cutting edges, e.g. of tools; Accessories therefor, e.g. for holding the tools of milling cutters
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Abstract
A four-axis grinding path generation method for a peripheral edge of a ball end mill comprises the following steps: firstly, determining a characteristic line of the peripheral edge of the ball cutter according to the contour of the peripheral edge of the ball cutter and the parameters of the spiral angle; step two, preparing a peripheral edge clearance angle parameter and a peripheral edge first width parameter of the ball cutter, wherein the parameters can be uniformly changed; thirdly, calculating a second characteristic line of the peripheral edge of the ball cutter, and calculating the top of the ball head in a segmented manner; fourthly, generating a four-axis grinding path of the peripheral edge of the ball cutter, and calculating the top of the ball head in a segmented manner; and fifthly, generating a second grinding path of the peripheral edge of the ball cutter, and calculating the top of the ball head in sections. The invention takes the idea of controlling the motion of each shaft of the machine tool and simplifies the peripheral edge grinding path into four-shaft linkage, thereby reducing the influence of the motion error of the machine tool on the rear tool face of the ball cutter and improving the precision of the rear tool face. The side edge part and the ball head part adopt the same path calculation method to ensure that the connecting part is smooth. The shape of the ball head is fully considered at the ball top, so that the characteristic line is positioned on the spherical surface, and good ball head profile is ensured.
Description
Technical Field
The invention relates to the field of cutter grinding, in particular to a four-axis grinding path generation method for a peripheral edge of a ball-end mill.
Background
The ball end mill is an efficient curved surface machining tool, is widely applied to the fields of automobiles, grinding tools, aviation and the like, and is more difficult to grind and more difficult to guarantee in precision compared with a flat-bottom end mill. When the ball cutter is used for milling, the cutter edge determined by the intersection line of the first rear cutter face and the front cutter face is directly related to the performance of the milling cutter and the processing quality of a milling workpiece. Therefore, the machining quality of the rear face of the ball cutter is very important in the whole grinding process of the ball cutter.
The rear cutter face of the ball cutter is generally machined by forming a complex cutter position track by using a standard grinding wheel and a complex multi-axis linkage machine tool, and the method has the advantages of complex cutter position track and higher requirement on the motion precision of the machine tool. Because five-axis linkage is difficult to reach higher grinding precision, if can reduce lathe motion axis quantity, will have qualitative promotion in the aspect of grinding precision and efficiency.
Meanwhile, the peripheral edge of the ball cutter comprises a side edge and a fillet, the side edge is generally designed with an equal helix angle, the fillet is designed with a variable helix angle, and the smooth transition problem of the connecting position of the side edge and the fillet is always a difficult problem in research, so that the grinding method of the side edge and the fillet is required to be the same in the peripheral sharpening process of the ball cutter. Meanwhile, the strength of the cutting edge of the ball cutter can be guaranteed by designing the offset of the bottom edge at the top of the ball head, if the top part of the ball head is not ground along the actual characteristic line, the grinding path at the cutting edge part needs special treatment, and the grinding path at the section is not smooth in transition and can seriously affect the profile degree of the ball cutter. In summary, whether the path is smooth or not is the key for determining the grinding precision of the ball cutter in the grinding process of the peripheral edge of the ball cutter.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and provides a four-axis grinding path method for the peripheral edge of a ball cutter, which ensures that a Y axis is not linked by controlling the motion of a B, C axis of a machine tool.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
firstly, determining a characteristic line of the peripheral edge of the ball cutter according to the spiral angle parameter and the profile parameter of the ball cutter;
step two, preparing a peripheral edge back angle parameter and a peripheral edge first width parameter of the ball cutter, wherein the two parameters can be uniformly changed;
thirdly, calculating a second characteristic line of the peripheral edge of the ball cutter based on the characteristic line of the peripheral edge I, the relief angle, the width and the offset of the bottom edge;
fourthly, generating a four-axis grinding path of the peripheral edge of the ball cutter, and calculating the top of the ball head in a segmented manner;
and fifthly, generating a second grinding path of the peripheral edge of the ball cutter, and calculating the top of the ball head in sections.
Further, the characteristic line calculation of the two ball head parts of the peripheral edge of the ball cutter in the third step is divided into two sections for processing. The characteristic line calculation is illustrated below:
step 1: determining the sectional position of a second peripheral edge characteristic line according to the critical 90-degree included angle between the tangent vector of the first peripheral edge characteristic line at the top of the ball head and the radius direction of the section circle of the point on the characteristic line;
step 2: establishing a back angle coordinate system according to the characteristic line of the peripheral edge, and taking the direction of the Y axis of the coordinate system rotating around the X axis by a back angle as the direction of a back angle line;
and step 3: the point on the characteristic line of the second peripheral edge is obtained by moving the first peripheral edge width along the direction of the relief angle line from the origin of the coordinate system.
The calculation method of the back angle coordinate system in the step 2 is explained as follows:
a. the origin of the coordinate system is a point on a characteristic line of the peripheral edge;
b. the Z axis of the coordinate system is the normal vector of the spherical surface of the ball cutter at the original point of the coordinate system;
c. the X axis of the coordinate system is the tangent vector of the spherical surface of the ball cutter at the generatrix of the origin of the coordinate system;
d. the Y-axis of the coordinate system is the Z-axis cross multiplied by the X-axis.
Particularly, because the tangent vector of the characteristic line of the peripheral edge of the ball top part is close to the tangent vector direction of the section circle of the characteristic line, the calculation method of the rear angle coordinate system is modified as follows:
a. the origin of the coordinate system is a point on a characteristic line of the peripheral edge;
b. the Z axis of the coordinate system is the normal vector of the spherical surface of the ball cutter at the original point of the coordinate system;
c. the Y axis of the coordinate system is a tangent vector of the spherical surface of the ball cutter on a section circle at the origin of the coordinate system;
d. the X-axis of the coordinate system is the Y-axis cross multiplied by the Z-axis.
Further, four-axis linkage is kept in a four-axis grinding path of the peripheral edge of the ball cutter in the fourth step, the Y axis of the four-axis linkage is not linked, the linkage shafts are X, Z, B, C axes respectively, and the main idea is as follows: and the Y coordinate of the machine tool is kept unchanged in the grinding process by controlling the swing angles of the B shaft and the C shaft of the machine tool. The grinding path calculation method comprises the following steps:
a. calculating the angle of the C shaft, rotating a point on a characteristic line of the peripheral edge to a horizontal position around the axis of the cutter, wherein the rotated angle is the angle C;
b. calculating a grinding point of the grinding wheel, wherein the grinding point of the grinding wheel is a fixed point on the circle with the largest cross section of the grinding wheel, and an included angle between the radial cross section where the fixed point is located and the horizontal cross section of the grinding wheel is a back angle value of a circumferential edge;
c. calculating a B-axis swing angle, and defining the B-axis swing angle as an included angle between a tangent vector of a characteristic line of the peripheral edge after rotating around the axis of the cutter and the axis of the cutter in order to ensure that the grinding wheel is tangent to the characteristic line;
d. determining the axial vector of the grinding wheel, and calculating the axial direction of the grinding wheel according to the B, C axial angle;
e. calculating the coordinates of the center point of the grinding wheel, contacting the grinding point of the grinding wheel with the point on the rotated characteristic line, and translating to obtain the coordinates of the center point of the grinding wheel;
f. and calculating the final grinding wheel pose, and rotating the axis of the grinding wheel and the coordinates of the center point of the grinding wheel around the Z axis by a negative C axis angle to obtain the final grinding wheel pose.
Particularly, the characteristic line of the top of the ball head needs to ensure the offset of the bottom edge and does not pass through the top of the ball, and the actual cutter needs to ensure that the outer contour is a complete circular arc, so that a four-axis grinding path of the peripheral edge of the ball cutter is processed in multiple sections.
In particular, the path of the peripheral edge-bulb top part is specially processed into a circular arc passing through the bulb top on the spherical surface.
In particular, the sectional position of the four-axis grinding path of the peripheral edge is determined according to the included angle between the tangent line of the characteristic line of the peripheral edge at a certain point and the radius direction of the section circle at the point, and the included angle is determined by the length of the bottom edge of the ball cutter and the offset of the bottom edge.
In particular, according to the set over-center distance, the four-axis grinding path of the peripheral edge also has a straight path which tangentially extends the path of the arc section at the top of the ball head besides the arc path section of the spherical surface.
Further, the fifth step of calculating the second grinding path of the peripheral edge of the ball cutter is as follows:
a. calculating the angle of the shaft C, rotating a point on a characteristic line of the first peripheral edge corresponding to the second peripheral edge to a horizontal position around the axis of the cutter, wherein the rotated angle is the angle C, and the point on the second peripheral edge is also rotated by the angle C;
b. calculating a grinding point of the grinding wheel, wherein the grinding point of the grinding wheel is a fixed point on the circle with the largest cross section of the grinding wheel, and an included angle between the radial cross section where the fixed point is located and the horizontal cross section of the grinding wheel is a peripheral edge two back angle value;
c. calculating a B-axis swing angle, and defining the B-axis swing angle as an included angle between a tangent vector of a characteristic line of the peripheral edge after rotating around the axis of the cutter and the axis of the cutter in order to ensure that the grinding wheel is tangent to the characteristic line;
d. determining the axial vector of the grinding wheel, and calculating the axial direction of the grinding wheel according to the B, C pivot angle;
e. calculating the coordinate of the center point of the grinding wheel, contacting the grinding point of the grinding wheel with the point on the two characteristic lines of the rotated peripheral edge, and translating to obtain the coordinate of the center point of the grinding wheel;
f. and calculating the final grinding wheel pose, and rotating the axis of the grinding wheel and the coordinates of the center point of the grinding wheel around the Z axis by a negative C axis angle to obtain the final grinding wheel pose.
Specifically, the ball cutter peripheral edge two-axis grinding path is processed in two stages at the ball head portion, and is segmented at the peripheral edge one-axis grinding path segment.
Particularly, the grinding path of the ball cutter peripheral edge II is a straight path in the subsection path of the top of the ball head.
Compared with the prior art, the peripheral edge grinding path of four-axis linkage is determined by controlling the motion of each axis of the machine tool, the influence of the motion error of the machine tool is smaller compared with the five-axis linkage path, and the precision of the rear tool face of the ball cutter can be improved. The flank face and the fillet flank face adopt the same grinding method, and the connection is smoother. The shape of the ball head is fully considered at the top part of the ball, so that the cutting edge is positioned on the spherical surface, the path is smooth in transition, and good ball head profile degree is guaranteed. Finally, the invention is applicable to end mills with complex profile profiles such as: the grinding machine is suitable for grinding the rear cutter face of the taper ball-head cutter and the barrel-shaped ball-head cutter, and can also be used for grinding the rear cutter face of a nose-shaped cutter and an end milling cutter.
Drawings
FIG. 1 is a pictorial view of a ball knife;
FIG. 2 is a schematic view of the swing angle of the C axis of the grinding wheel;
FIG. 3 is a schematic view of a grinding point of the grinding wheel;
FIG. 4 is a schematic view of the grinding wheel B axis swing angle;
fig. 5 is a fragmentary schematic view of a ball top grinding path.
Detailed Description
The details of the technical solution proposed by the present invention will be described in detail below with reference to the accompanying drawings. The description is illustrative of the invention and is not to be construed as limiting.
The invention provides a four-axis grinding path generation method for a peripheral edge of a ball end mill, which is realized by the following measures:
firstly, determining a characteristic line of the peripheral edge of the ball cutter through the spiral angle parameter and the profile parameter of the ball cutter. The characteristic line of the circumferential edge is calculated by a conventional spiral line at the side edge part, namely, the included angle between the tangent line of the characteristic line and the axis of the cutter is a spiral angle, the ball head part is designed by a variable spiral angle, the spiral angle of the ball top part is 90 degrees, the offset of the bottom edge is required to be considered at the ball top part, and the ball top spiral line can be calculated according to the definition of the spiral angle;
and step two, preparing a ball cutter circumferential edge back angle parameter and a circumferential edge first width parameter, wherein the two parameters can be uniformly changed. That is, the values of the parameters at a plurality of positions can be proportionally given on the whole circumferential edge, and the values are uniformly distributed to each point on the circumferential edge;
and thirdly, calculating a second characteristic line of the peripheral edge of the ball cutter based on the characteristic line of the peripheral edge, the relief angle, the width and the offset of the bottom edge. The characteristic line of the first peripheral edge is obtained by translating a point on the first peripheral edge along the direction of the relief angle line by the relief angle width;
fourthly, generating a four-axis grinding path of the peripheral edge of the ball cutter, and calculating the top of the ball head in a segmented manner;
and fifthly, generating a second grinding path of the peripheral edge of the ball cutter, and calculating the top of the ball head in sections.
The fourth step is specifically described as follows:
step 1: and calculating the C-axis rotating angle, and referring to FIG. 2, the coordinates of the characteristic points on the first circumferential edge are represented as:
when the point rotates to the horizontal position (on the XOZ surface) around the Z axis, the rotating angle is the C axis rotating angle, and the calculation formula is as follows:
. Particularly, if the segmented position of one path of the peripheral edge is closer to the top of the sphere than the segmented position of the second characteristic line of the peripheral edge, in order to ensure that the change of the C-axis angle is uniform after the segmented position of the second characteristic line of the peripheral edge, the C-axis angle is determined by adopting a method that tangent vectors at characteristic points replace the characteristic points to rotate to a horizontal position;
step 2: calculating a grinding wheel grinding point, referring to fig. 3, in order to avoid the grinding interference problem, determining that the grinding wheel grinding point is located on a circle where the maximum section radius of the grinding wheel is located, and the grinding wheel grinding point of the 0-degree relief angle ball cutter is located on the negative X axis shown in fig. 3, wherein the grinding wheel grinding point is kept unchanged in the whole grinding process;
and step 3: and (4) calculating the B-axis swing angle, referring to fig. 4, and defining an included angle between the tangent vector of the characteristic point and the Z axis after the grinding wheel rotates to the horizontal position as the B-axis swing angle of the grinding wheel. Particularly, because the tangent vector of the characteristic line of the side edge part of the common ball cutter is the same as the axial direction of the cutter arbor, the B-axis swing angle is 0, and the only grinding wheel position cannot be determined during post-processing, the clearance angle parameter is increased to determine the final B-axis swing angle;
and 4, step 4: converting the B, C shaft angle into a vector, namely a grinding wheel axis vector;
and 5: calculating the coordinate of the center point of the grinding wheel, and translating the grinding wheel to enable the grinding point of the grinding wheel in the step 2 to be in contact with the characteristic point after the grinding wheel rotates around the Z axis by an angle C in the step 1
Contacting to obtain the coordinates of the central point of the grinding wheel;
step 6: and rotating the coordinates of the central point of the grinding wheel and the axial vector of the grinding wheel around the Z axis by a negative C angle to obtain the final pose of the grinding wheel.
The fifth step is the same as the fourth step in the calculation flow, and the relief angle used when calculating the grinding wheel grinding position only in step 2 is the secondary relief angle of the peripheral edge.
The four-axis grinding path generation method for the peripheral edge provided by the invention relates to the step of path segmentation processing, and referring to fig. 5, the segmentation position of the peripheral edge on one path is determined according to the included angle between the tangent vector of the characteristic line and the radius direction of the point on the characteristic line, and the size of the included angle can be specified. The sectional grinding path of the peripheral edge is a circular arc path passing through the sectional position and the top of the ball. The two-section grinding path of the peripheral edge can be simplified into a straight path of the grinding wheel axis and the axis direction of the point at the section, and the movement position of the grinding wheel is a tangent line along the point at the section.
Claims (10)
1. A four-axis grinding path generation method for a peripheral edge of a ball end mill is characterized by comprising the following steps:
firstly, determining a characteristic line of the peripheral edge of the ball cutter according to the spiral angle parameter and the profile parameter of the ball cutter;
step two, preparing a peripheral edge back angle parameter and a peripheral edge first width parameter of the ball cutter, wherein the two parameters can be uniformly changed;
thirdly, calculating a second characteristic line of the peripheral edge of the ball cutter based on the characteristic line of the peripheral edge I, the relief angle, the width and the offset of the bottom edge;
fourthly, generating a four-axis grinding path of the peripheral edge of the ball cutter, and calculating the top of the ball head in a segmented manner;
and fifthly, generating a second grinding path of the peripheral edge of the ball cutter, and calculating the top of the ball head in sections.
2. The four-axis grinding path generation method for the peripheral edge of the ball nose end mill according to claim 1, wherein the two-axis characteristic line of the peripheral edge of the ball nose is calculated and processed in two stages at the top of a ball head, and the calculation step is as follows: determining the sectional position of a second peripheral edge characteristic line according to the critical 90-degree included angle between the tangent vector of the first peripheral edge characteristic line at the top of the ball head and the radius direction of the section circle of the point on the characteristic line; establishing a back angle coordinate system O-XYZ according to a characteristic line of the peripheral edge, and taking the direction of the back angle of the Y axis of the coordinate system rotating around the X axis as the direction of the back angle line; the point on the characteristic line of the second peripheral edge is obtained by moving the original point of the coordinate system along the direction of the relief angle line by the width of the first peripheral edge, wherein the calculation step of the relief angle coordinate system O-XYZ is as follows:
the origin of the coordinate system is a point on the first peripheral edge;
the Z axis of the coordinate system is the normal vector of the spherical surface of the ball cutter at the original point of the coordinate system;
the X axis of the coordinate system is the tangent vector of the spherical surface of the ball cutter at the generatrix of the origin of the coordinate system;
the Y axis of the coordinate system is the X axis multiplied by the Z axis;
because the tangent vector of the characteristic line of the peripheral edge of the spherical top part is close to the tangent vector direction of the section circle of the characteristic line, the calculation method of the spherical top part rear angle coordinate system is modified as follows:
the origin of the coordinate system is a point on the first peripheral edge;
the Z axis of the coordinate system is the normal vector of the spherical surface of the ball cutter at the original point of the coordinate system;
the Y axis of the coordinate system is a tangent vector of the spherical surface of the ball cutter on a section circle at the origin of the coordinate system;
the X-axis of the coordinate system is the Y-axis cross multiplied by the Z-axis.
3. The four-axis grinding path generating method of a peripheral edge of a ball nose end mill according to claim 1, characterized in that: the four-axis grinding path of the peripheral edge of the ball cutter keeps four-axis linkage, the Y axis of the ball cutter is not linked, the linkage shafts are X, Z, B, C axes respectively, and the specific calculation method comprises the following steps:
calculating the angle of the C shaft, rotating a point on a characteristic line of the peripheral edge to a horizontal position around the axis of the cutter, wherein the rotated angle is the angle C;
calculating a grinding point of the grinding wheel, wherein the grinding point of the grinding wheel is a fixed point on the circle with the largest cross section of the grinding wheel, and an included angle between the radial cross section where the fixed point is located and the horizontal cross section of the grinding wheel is a back angle value of a circumferential edge;
calculating a B-axis swing angle, and defining the B-axis swing angle as an included angle between a tangent vector of a characteristic line of the peripheral edge after rotating around the axis of the cutter and the axis of the cutter in order to ensure that the grinding wheel is tangent to the characteristic line;
determining the axial vector of the grinding wheel, and calculating the axial direction of the grinding wheel according to the B, C axial angle;
calculating the coordinate of the center point of the grinding wheel, contacting the grinding point of the grinding wheel with the point on the rotated characteristic line, and translating to obtain the coordinate of the center point of the grinding wheel;
and calculating the final grinding wheel pose, and rotating the axis of the grinding wheel and the coordinates of the center point of the grinding wheel around the Z axis by a negative C axis angle to obtain the final grinding wheel pose.
4. The four-axis grinding path generation method for a peripheral edge of a ball nose end mill according to claim 3, characterized in that: the four-axis grinding path of the peripheral edge of the ball cutter is processed in multiple sections.
5. The four-axis grinding path generation method for a peripheral edge of a ball nose end mill according to claim 4, characterized in that: the four-axis grinding path of the peripheral edge of the ball cutter is specially processed into an arc path passing through the top of the ball on the spherical surface at the top part of the ball head.
6. The four-axis grinding path generation method for a peripheral edge of a ball nose end mill according to claim 4, characterized in that: the sectional position of the four-axis grinding path of the peripheral edge of the ball cutter is determined according to an included angle between a tangent line of a characteristic line of the peripheral edge at a certain point and the radius direction of a section circle at the point, and the included angle is determined by the length of the bottom edge of the ball cutter and the offset of the bottom edge.
7. The four-axis grinding path generation method for a peripheral edge of a ball nose end mill according to claim 4, characterized in that: the four-axis grinding path of the peripheral edge of the ball cutter is a straight line path which is arranged at the top of the ball head and is used for tangentially extending the path of the arc section besides the arc path section of the spherical surface.
8. The four-axis grinding path generating method of a peripheral edge of a ball nose end mill according to claim 1, characterized in that: the calculation method of the grinding path of the peripheral edge II of the ball cutter comprises the following steps:
calculating the angle of the shaft C, rotating a point on a characteristic line of the first peripheral edge corresponding to the second peripheral edge to a horizontal position around the axis of the cutter, wherein the rotated angle is the angle C, and the point on the second peripheral edge is also rotated by the angle C;
calculating a grinding point of the grinding wheel, wherein the grinding point of the grinding wheel is a fixed point on the circle with the largest cross section of the grinding wheel, and an included angle between the radial cross section where the fixed point is located and the horizontal cross section of the grinding wheel is a peripheral edge two back angle value;
calculating a B-axis swing angle, and defining the B-axis swing angle as an included angle between a tangent vector of a characteristic line of the peripheral edge after rotating around the axis of the cutter and the axis of the cutter in order to ensure that the grinding wheel is tangent to the characteristic line;
determining the axial vector of the grinding wheel, and calculating the axial direction of the grinding wheel according to the B, C pivot angle;
calculating the coordinate of the center point of the grinding wheel, contacting the grinding point of the grinding wheel with the point on the two characteristic lines of the rotated peripheral edge, and translating to obtain the coordinate of the center point of the grinding wheel;
and calculating the final grinding wheel pose, and rotating the axis of the grinding wheel and the coordinates of the center point of the grinding wheel around the Z axis by a negative C axis angle to obtain the final grinding wheel pose.
9. The four-axis grinding path generating method of a peripheral edge of a ball nose end mill according to claim 8, characterized in that: the grinding path of the peripheral edge two of the ball cutter is processed in two sections at the ball head part, and is segmented at the grinding path of the peripheral edge one of the four shafts.
10. The four-axis grinding path generating method of a peripheral edge of a ball nose end mill according to claim 8, characterized in that: the grinding path of the second peripheral edge of the ball cutter is a straight path at the top of the ball head.
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