CN107563002B - Method for fitting and forming cutting edge curve of milling cutter - Google Patents
Method for fitting and forming cutting edge curve of milling cutter Download PDFInfo
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- CN107563002B CN107563002B CN201710646317.6A CN201710646317A CN107563002B CN 107563002 B CN107563002 B CN 107563002B CN 201710646317 A CN201710646317 A CN 201710646317A CN 107563002 B CN107563002 B CN 107563002B
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Abstract
The invention discloses a method for fitting and forming a cutting edge curve of a milling cutter, which comprises the steps of drawing an initial circular arc ab and drawing a straight line bOabDrawing an auxiliary arc bc' passing through the center O of the auxiliary arc bcbc’Drawing a reference search straight line L0Drawing circular arc bc0Judging circular arc bc0Whether the fitting precision requirement is met or not and the searching step length T is set for searching the circular arc bcnAnd obtaining the solved circular arc bc, obtaining the solved circular arcs cd, de, ef and … … according to the same method, completing the fitting of the whole spline curve and the like.
Description
Technical Field
The invention relates to the technical field of material cutting processing, in particular to a method for fitting and forming a cutting edge curve of a milling cutter.
Background
The integral hard alloy formed milling cutter is widely applied to the 3C industry, such as the processing of shells of smart phones, tablet computers, notebooks and the like, and the appearance surface of the product is basically formed by spline curves for the reasons of attractiveness, convenience in holding and the like. According to the metal cutting principle, the shape of the cutting edge of the formed milling cutter is completely reproduced on a product, so that the ideal state is that the cutting edge curve of the formed milling cutter is completely consistent with the spline curve of the shell of a 3C product. However, due to the limitation of the CNC (computerized numerical control) grinding machine, the machine tool program cannot directly accept the spline curve, so the arc which can be accepted by the machine tool program is required to be used for fitting the spline curve by using CAD (computer-aided design) software, but the fitting method in the prior art has large error of the formed cutting edge curve, and the fitted arc is easy to have the problem of incongruity, so that a sharp point exists at the joint of the two arcs, and the existence of the sharp point can leave a scratch on the surface of a part on one hand, so that the appearance attractiveness of a 3C product is poor; on the other hand, premature wear of the cutting edge can also result, reducing tool life.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art and provide a method for fitting and forming the cutting edge curve of the milling cutter, wherein the fitted curve has no sharp point and high fitting precision.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for fitting and forming a cutting edge curve of a milling cutter adopts computer graphics software and comprises the following steps:
s1: taking any endpoint a of the spline curve as a starting point, and drawing an initial circular arc ab of which the maximum normal error h between the initial circular arc ab and the spline curve is less than the fitting precision requirement;
s2: end point b and center O of initial arc ababMaking a straight line bOab；
S3: drawing an auxiliary arc bc' by taking the end point b of the initial arc ab as a starting point and passing through the center O of the auxiliary arc bcbc’Drawing a reference search straight line L0Let a reference search line L0And the straight line bOabHas an intersection of X0；
S4: with X0Drawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting point0；
S5: judging circular arc bc0Whether the maximum normal error h between the arc and the spline curve meets the fitting precision requirement or not is judged, and if the maximum normal error h meets the fitting precision requirement, the arc bc is determined0That is, the arc bc is obtained, and the process proceeds to step S7, and if not, the process proceeds to step S6;
s6: setting a search step length T and drawing a search straight line L parallel to the reference0Is searched for a straight line LnSearch for a straight line LnAnd reference search straight line L0The distance between the two is nT, and a search straight line L is setnAnd the straight line bOabHas an intersection of XnWith XnDrawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting pointnJudging the circular arc bcnWhether the maximum normal error h between the arc and the spline curve meets the fitting precision requirement or not is judged, and if the maximum normal error h meets the fitting precision requirement, the arc bc is determinednThat is, the desired arc bc, and proceeds to step S7, and if not, follows this stepThe method in step draws the circular arc bcn+1Until the required circular arc bc is obtained, in this step, n =1, 2, 3, … …;
s7: and taking the end point c of the obtained circular arc bc as a starting point, and sequentially obtaining the obtained circular arcs cd, de, ef and … … by the same method from S2 to S6 until the fitting of the whole sample curve is completed.
As a further improvement of the above technical solution:
in step S6, fitting is performed in the order of n from small to large.
In said step S3, the maximum normal error of the auxiliary arc bc' with the spline curve is not more than the same order of magnitude as the fitting accuracy requirement.
In the step S3, the reference search straight line L0Perpendicular to the straight line bOab。
In step S6, the search step length T is less than or equal to 1 mm.
In step S6, for each value of n, a straight line L is searched for at its reference0One fitting is performed on each side of the panel.
Compared with the prior art, the invention has the advantages that:
(1) the method for fitting and forming the cutting edge curve of the milling cutter provided by the invention is used for forming the cutting edge curve of the milling cutter if the circular arc bc0The maximum normal error h between the target point and the spline curve meets the requirement of fitting precision, namely the required circular arc bc because of the circular arc bc0Having a common end point b with the initial arc ab, and an arc bc0Has a center of a circle of X0The center of the initial arc ab is OabAnd O isabAnd X0Are all located on a straight line bOabUp, therefore, the circular arc bc0Must be tangent to the initial arc ab, and the tangent point is the end point b if the arc bc0If the circular arc bc is not the desired circular arc bc, the circular arc bc is searched for by step S6nUp to the arc bcnThe maximum normal error h between the normal error and the spline curve meets the requirement of fitting precision, namely the circular arc bcnFor the circular arc bc sought, since the circular arc bcnHaving a common end point b with the initial arc ab, and an arc bcnCenter of circle X ofnFrom the centre O of the initial arc ababAre all located on a straight line bOabUp, therefore, the circular arc bcnThe cutting edge curve of the whole formed milling cutter obtained by the fitting method of the invention meets the precision requirement and has no sharp point, namely the method for fitting the cutting edge curve of the formed milling cutter has high fitting precision.
(2) The method for fitting and forming the cutting edge curve of the milling cutter draws the auxiliary arc bc ', and only by ensuring that the maximum normal error h of the auxiliary arc bc' and the spline curve is in the same order of magnitude as the fitting precision requirement, the arc bc is determinednThe search range is reduced, and then a search straight line L is drawn by setting a search step length TnAnd the straight line bOabIntersect to form an arc bcnThe circle center Xn improves the searching efficiency, and only bc can be determined if the auxiliary arc bc' is not drawnnIs centered on the straight line bOabAnd the approximate range cannot be determined, and if the arc bc which meets the fitting precision requirement and is tangent to the arc ab is to be found, a large amount of search is needed, so that the efficiency is low.
Drawings
FIG. 1 is a schematic diagram of steps S1 and S2 of the present invention.
Fig. 2 is a schematic diagram of step S3 according to the present invention.
Fig. 3 is a schematic diagram of step S4 according to the present invention.
FIG. 4 is a drawing of arc bc in step S6 of the present invention1Schematic representation of (a).
FIG. 5 is a drawing of arc bc in step S6 of the present inventionnSchematic representation of (a).
Fig. 6 is a schematic diagram of step S7 of the present invention.
The reference numerals in the figures denote:
1. spline curve.
Detailed Description
The invention will be described in further detail below with reference to the drawings and specific examples.
The method for fitting and forming the cutting edge curve of the milling cutter adopts computer mapping software and comprises the following steps:
s1: taking any endpoint a of the spline curve as a starting point, and drawing an initial circular arc ab of which the maximum normal error h between the initial circular arc ab and the spline curve is less than the fitting precision requirement;
s2: end point b and center O of initial arc ababMaking a straight line bOab；
S3: drawing an auxiliary arc bc' by taking the end point b of the initial arc ab as a starting point and passing through the center O of the auxiliary arc bcbc’Drawing a reference search straight line L0Let a reference search line L0And the straight line bOabHas an intersection of X0；
S4: with X0Drawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting point0；
S5: judging circular arc bc0Whether the maximum normal error h between the arc and the spline curve meets the fitting precision requirement or not is judged, and if the maximum normal error h meets the fitting precision requirement, the arc bc is determined0That is, the arc bc is obtained, and the process proceeds to step S7, and if not, the process proceeds to step S6;
s6: setting a search step length T and drawing a search straight line L parallel to the reference0Is searched for a straight line LnSearch for a straight line LnAnd reference search straight line L0The distance between the two is nT, and a search straight line L is setnAnd the straight line bOabHas an intersection of XnWith XnDrawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting pointnJudging the circular arc bcnWhether the maximum normal error h between the arc and the spline curve meets the fitting precision requirement or not is judged, and if the maximum normal error h meets the fitting precision requirement, the arc bc is determinednThat is, the circular arc bc is obtained, and the procedure goes to step S7, if not, the circular arc bc is drawn according to the method in this stepn+1Until the required circular arc bc is obtained, in this step, n =1, 2, 3, … …;
s7: and taking the end point c of the obtained circular arc bc as a starting point, and sequentially obtaining the obtained circular arcs cd, de, ef and … … by the same method from S2 to S6 until the fitting of the whole sample curve is completed.
If the arc bc0The maximum normal error h between the target point and the spline curve meets the requirement of fitting precision, namely the required circular arc bc because of the circular arc bc0Having a common end point b with the initial arc ab, and an arc bc0Has a center of a circle of X0The center of the initial arc ab is OabAnd O isabAnd X0Are all located on a straight line bOabUp, therefore, the circular arc bc0Must be tangent to the initial arc ab, and the tangent point is the end point b if the arc bc0If the circular arc bc is not the desired circular arc bc, the circular arc bc is searched for by step S6nUp to the arc bcnThe maximum normal error h between the normal error and the spline curve meets the requirement of fitting precision, namely the circular arc bcnFor the circular arc bc sought, since the circular arc bcnHaving a common end point b with the initial arc ab, and an arc bcnCenter of circle X ofnFrom the centre O of the initial arc ababAre all located on a straight line bOabUp, therefore, the circular arc bcnThe cutting edge curve of the whole formed milling cutter obtained by the fitting method of the invention not only meets the precision requirement, but also has no sharp point, namely the method for fitting the cutting edge curve of the formed milling cutter has high fitting precision, and the formed milling cutter manufactured by the method has good processing quality and long service life.
In step S6, fitting is performed in the order of n from small to large, and in the process, it is determined to continue searching for the straight line L on the basis according to the variation trend of the maximum normal error h0The same side of the line is fitted according to the sequence of n from small to large, or the searching direction is changed, and a straight line L is searched in the reference0The other side of the search begins.
In step S3, the maximum normal error h of the auxiliary arc bc' and the spline curve is not greater than the same order of magnitude as the fitting accuracy requirement, i.e., the arc bc is determinednThe approximate range of the circle center is reduced, the search range is narrowed, and a search straight line L is drawn by setting a search step length TnAnd the straight line bOabIntersect to form an arc bcnThe circle center Xn improves the searching efficiency, and only bc can be determined if the auxiliary arc bc' is not drawnnIs centered on the straight line bOabAnd the approximate range cannot be determined, and if the arc bc which meets the fitting precision requirement and is tangent to the arc ab is to be found, a large amount of search is needed, so that the efficiency is low.
In step S3, the reference search straight line L0Perpendicular to the straight line bOab。
In step S6, the search step T is less than or equal to 1mm, and the value of the search step T should be as small as possible during the actual fitting process to ensure that the arc to be found that is closest to the spline curve 1 can be found, thereby improving the fitting accuracy.
In step S6, for each value of n, a straight line L is searched for at its reference0One fitting is performed on each side of the panel.
Fig. 1 to 6 show an embodiment of fitting a spline curve by the method for fitting and forming the cutting edge curve of the milling cutter, as shown in fig. 1, the fitting accuracy requirement of the spline curve 1 is 0.01mm, the right end point a of the spline curve 1 is taken as a starting point, an initial circular arc ab with a maximum normal error h between the initial circular arc ab and the spline curve 1 smaller than the fitting accuracy requirement is drawn, and the end point b and the circle center O of the initial circular arc ab are passed throughabMaking a straight line bOab。
As shown in fig. 2, the endpoint b of the initial arc ab is used as a starting point to draw the auxiliary arc bc ', in this embodiment, the maximum normal error h between the auxiliary arc bc' and the spline curve 1 is 0.06mm, which is not greater than the same order of magnitude required by the fitting accuracy, and passes through the center O of the auxiliary arc bcbc’Drawing a reference search straight line L0Let a reference search line L0And the straight line bOabHas an intersection of X0In the actual operation process, the arc length of the auxiliary arc bc' should be as short as possible, and the maximum normal error h should be as small as possible.
As shown in FIG. 3, with X0Drawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting point0And judging to obtain the circular arc bc0The maximum normal error h between the spline curve 1 and the spline curve is 0.03mm, and the fitting precision requirement is not met.
Therefore, as shown in fig. 4, setting the search step T =0.41mm, the reference search straight line L is drawn in parallel0Is searched for a straight line L1Search for a straight line L1And reference search straight line L0The distance between the two is T (namely 0.41 mm), and a search straight line L is set1And the straight line bOabHas an intersection of X1With X1Drawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting point1And judging to obtain the circular arc bc1The maximum normal error h between the curve and the spline curve 1 is 0.019mm, does not meet the requirement of fitting precision, but is relative to the circular arc bc0Since the error is reduced, a straight line L is searched for as shown in fig. 51Continues searching on the same side, draws a straight line L parallel to the reference search0Is searched for a straight line L2Search for a straight line L2And reference search straight line L0The distance between the two is 2T (namely 0.82 mm), and a search straight line L is set2And the straight line bOabHas an intersection of X2With X2Drawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting point2And judging to obtain the circular arc bc2The maximum normal error h between the spline curve 1 and the maximum normal error h is 0.014mm, the fitting precision requirement is not met, and the search is continued until the circular arc bc is drawn4And judging to obtain the circular arc bc4The maximum normal error h between the spline curve 1 and the arc bc is 0.009mm, and meets the fitting precision requirement4I.e. the desired arc bc.
As shown in fig. 6, the arcs cd, de, ef, and … … are obtained in turn by the same method until the fitting of the entire spline curve is completed.
Comparing the formed milling cutter processed by the method of the present invention with the formed milling cutter in the prior art, the following can be obtained: the cutting edges of the formed milling cutter designed by the method are perfectly tangent without sharp points, and the processed surface has excellent quality and long service life; the cutting edge curve of the formed milling cutter in the prior art is not tangent and has a sharp point, and the sharp point is easy to scratch the surface of a part in the process of processing the part, so that the appearance is influenced, and the service life of the formed milling cutter is short.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Those skilled in the art can make numerous possible variations and modifications to the present invention, or modify equivalent embodiments to equivalent variations, without departing from the scope of the invention, using the teachings disclosed above. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical spirit of the present invention should fall within the protection scope of the technical scheme of the present invention, unless the technical spirit of the present invention departs from the content of the technical scheme of the present invention.
Claims (4)
1. A method for fitting and forming a cutting edge curve of a milling cutter adopts computer graphics software, and is characterized by comprising the following steps:
s1: taking any endpoint a of the spline curve as a starting point, and drawing an initial circular arc ab of which the maximum normal error h between the initial circular arc ab and the spline curve is less than the fitting precision requirement;
s2: end point b and center O of initial arc ababDrawing a straight line bOab；
S3: drawing an auxiliary arc bc ' by taking an endpoint b of the initial arc ab as a starting point, wherein the maximum normal error h of the auxiliary arc bc ' and the spline curve is not more than the same order of magnitude required by fitting precision, and the auxiliary arc bc ' passes through the center O of the auxiliary arc bcbc’Drawing a reference search straight line L0Reference search straight line L0Perpendicular to the straight line bOabLet a reference search line L0And the straight line bOabHas an intersection of X0；
S4: with X0Drawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting point0；
S5: judging circular arc bc0Whether the maximum normal error h between the arc and the spline curve meets the fitting precision requirement or not is judged, and if the maximum normal error h meets the fitting precision requirement, the arc bc is determined0That is, the arc bc is obtained, and the process proceeds to step S7, and if not, the process proceeds to step S6;
s6: setting a search step length T and drawing a search straight line L parallel to the reference0Is searched for a straight line LnSearch for a straight line LnAnd reference search straight line L0The distance between the two is nT, and a search straight line L is setnAnd the straight line bOabHas an intersection of XnWith XnDrawing an arc bc with the center of circle and the end point b of the initial arc ab as a starting pointnJudging the circular arc bcnWhether the maximum normal error h between the arc and the spline curve meets the fitting precision requirement or not is judged, and if the maximum normal error h meets the fitting precision requirement, the arc bc is determinednThat is, the circular arc bc is obtained, and the procedure goes to step S7, if not, the circular arc bc is drawn according to the method in this stepn+1Until the required circular arc bc is obtained, in the step, n is equal to any natural number;
s7: and taking the end point c of the solved circular arc bc as a starting point, and sequentially obtaining the solved circular arcs cd, de and ef and subsequent solved circular arcs by the same method from S2 to S6 until the fitting of the whole spline curve is completed.
2. The method of fitting a profile milling cutter edge curve according to claim 1, wherein: in step S6, fitting is performed in the order of n from small to large.
3. The method of fitting a profiled milling cutter edge curve according to claim 1 or 2, wherein: in step S6, the search step length T is less than or equal to 1 mm.
4. The method of fitting a profiled milling cutter edge curve according to claim 1 or 2, wherein: in step S6, for each value of n, a straight line L is searched for at its reference0One fitting is performed on each side of the panel.
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| CN201710646317.6A CN107563002B (en) | 2017-08-01 | 2017-08-01 | Method for fitting and forming cutting edge curve of milling cutter |
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| CN111102897B (en) * | 2019-11-29 | 2022-04-12 | 中国航发沈阳黎明航空发动机有限责任公司 | Arc block part fitting analysis method |
| CN114065316B (en) * | 2021-10-20 | 2023-10-31 | 中国航发四川燃气涡轮研究院 | Method for calculating common tangent circle of two curves in plane |
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| US20110250025A1 (en) * | 2003-10-15 | 2011-10-13 | Tdy Industries, Inc. | Cutting insert for high feed face milling |
| CN105651200A (en) * | 2016-01-08 | 2016-06-08 | 大连理工大学 | Data selection method for calculating blunt round radius of cutting edge |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110250025A1 (en) * | 2003-10-15 | 2011-10-13 | Tdy Industries, Inc. | Cutting insert for high feed face milling |
| CN105651200A (en) * | 2016-01-08 | 2016-06-08 | 大连理工大学 | Data selection method for calculating blunt round radius of cutting edge |
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| A Method of Circle Curve Fitting Based on the Cumulative Error of the Radius Error;Chunlong Fan等;《2015 11th International Conference on Computational Intelligence and Security (CIS)》;20160204;全文 * |
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