CN103676788A - Smooth processing-oriented numerical control processing track processing method - Google Patents
Smooth processing-oriented numerical control processing track processing method Download PDFInfo
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Abstract
The invention discloses a smooth processing-oriented numerical control processing track processing method. The method comprises the following steps of step 1, traversing all the small line sections on the whole processing track, and judging interpolation subintervals; step 2, performing interpolation calculation on the small line sections in the interpolation subintervals by an arc interpolation method; step 3, traversing all the small line sections on the whole processing track, and judging smooth filtration subintervals; step 4, performing filtration on each corner required to be subjected to smooth filtration by moving filtration technology. The requirement on real-time property of a numerical control system can be met, and the special requirement of smooth processing on a processed track can be met.
Description
Technical field
The present invention relates to numerical control processing track processing technology field, particularly relate to a kind of numerical control processing track disposal route towards fairing processing.
Background technology
Different processing types is also different to the requirement of digital control processing, as mostly pursued the fastest process velocity in wood carving processing, to the smooth finish of machining precision and finished surface, requires lower; In the processing of exact instrument accessory, more value machining precision, can in the process of processing, sacrifice certain speed to exchange higher machining precision for; Yet in the process of part module, the smooth finish of finished surface is its most important evaluation index.Conventionally, process velocity, precision and surface smoothness are the evaluation indexes of three mutual exclusions.Therefore,, in order to improve the wherein performance of certain index, often need to sacrifice the performance of other two indexs.In order to address this problem, the numerical control machining scheme that existing part is preferential for working (machining) efficiency and machining precision is preferential proposes.But it is less that in existing digital control processing, effects on surface smooth finish is processed the support of preferential cooked mode, the assurance of smooth finish is main or the polishing in later stage completes by processing.Obviously, manual polishing velocity is relatively slow, and this has had a strong impact on working (machining) efficiency.
In digital control processing, the surface of module to be processed is generally combined by some planes and free form surface, and numerically-controlled machine can only be controlled the motion that cutter completes point-to-point.Therefore, when complete the modeling for the treatment of processing module in CAD after, need to first be sent into CAM system, will treat that curved surface is separated into the track to be processed that digital control system can be identified, complete path planning operation, and then the machining locus of generation is sent into and in digital control system, completed processing.
When CAM system completes machining path planning, the most frequently used method is to wait scallop-height method, and its main thought is according to given maximum scallop-height (tolerance) and tool radius, with a series of cutter path, removes to cover whole processing curve.When the smooth finish of finished surface is had relatively high expectations, less maximum scallop-height generally can be set, the method that improves machining precision is improved the smooth finish of finished surface.Under this set, the total path length of generation is elongated, and the length of the little line segment of wall scroll shortens.Yet although improve the fairness that the precision of finished surface contributes to improve finished surface, fairing and precision are not two concepts of equal value.The machining precision on surface refers to the maximum scallop-height on finished surface, and fairing is embodied on machining path seamlessly transitting of turning between little line segment more.
Therefore,, for above-mentioned technical matters, need to propose a kind of numerical control processing track disposal route towards fairing processing, thereby obtain more bright and clean part finished surface.
Summary of the invention
In view of this, in order to solve the existing deficiency to fairing working research, the present invention will not meet this problem of fairing processing conditions for existing Machining Path, the fairing problem of pretreatment of research Machining Path, by introducing circular interpolation technology and glide filter technology, provide a kind of numerical control processing track disposal route towards fairing processing.
To achieve these goals, the technical scheme that the embodiment of the present invention provides is as follows:
A numerical control processing track disposal route towards fairing processing, said method comprising the steps of:
All little line segment on S1, traversal whole piece machining locus, carries out the judgement in interpolation sub-range;
S2, to the little line segment in interpolation sub-range, adopt the method for circular interpolation to carry out interpolation calculation.
As a further improvement on the present invention, described step S1 specifically comprises:
Little line segment on S11, traversal whole piece machining locus;
S12, the little line segment length of the shortest interpolation of setting;
S13, judge that whether current traversed little line segment length is greater than the little line segment length of the shortest interpolation setting, and if so, carries out S14; Otherwise, carry out S18;
S14, set maximum turning;
S15, judge that whether the turning size of little line segment destination county is less than the maximum turning setting, and if so, carries out S16; Otherwise, carry out S18;
S16, this little line segment is joined in interpolation sub-range;
S17, obtain needing the little line segment aggregate of interpolation calculation;
S18, obtain not needing the little line segment aggregate of interpolation calculation.
As a further improvement on the present invention, described step S2 specifically comprises:
S21, obtain the little line segment in interpolation sub-range;
S22, with one section of circular arc, approach original little line segment;
The direction of S23, judgement circular arc;
S24, obtain the expression formula of circular arc;
S25, obtain the expression formula of interpolation circular arc;
S26, at the enterprising row interpolation of circular arc, calculate, obtain interpolation point.
As a further improvement on the present invention, after described step S2, also comprise:
All little line segment on S3, traversal whole piece machining locus, carries out the judgement in fairing filtering sub-range;
S4, to carrying out each turning of fairing filtering, adopt glide filter technology to carry out filtering.
As a further improvement on the present invention, described step S3 is specially:
S31, travel through the tracing point on every paths;
S32, according to direction between little line segment, change and should meet conforming principle whole piece machining locus is divided into several sub-ranges;
S33, judge in sub-range whether at least exist two turnings between adjacent little line segment to be less than preset value, if so, to carry out S34; Otherwise, carry out S35;
S34, obtain needing the set in the sub-range of fairing filtering;
S35, obtain not needing the set in the sub-range of fairing filtering.
As a further improvement on the present invention, described step S4 is specially:
S41, moving window N is set
w;
S42, obtain the result output of this cycle glide filter;
S43, to the variation of little line segment angle, adopt moving average filter to carry out filtering.
As a further improvement on the present invention, in described step S42, for the little line segment of i bar on filtering sub-range, Output rusults is:
and N
jmeet N
j=min (i+N
w, N), wherein, the number that N is little line segment.
Numerical control processing track disposal route towards fairing processing of the present invention, glide filter technology and interpolation technique are incorporated in the fairing processing problem of Machining Path, at the machining path little line segment not being formed, fit on the basis of curve, design a kind of pre-service mechanism in continually varying fairing path, turning between adjacent little line segment that realizes on machining path.For the machining locus with different characteristics, adopt different preprocess methods.For example, for the longer machining locus of the little line segment of wall scroll, adopt the mode of interpolation, and for the shorter machining locus of the little line segment of wall scroll, further adopt the mode of glide filter to reduce low-angle tracing point transition, meet the requirement of digital control system real-time, strengthen the adaptability of fairing processing function.
Accompanying drawing explanation
In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, to the accompanying drawing of required use in embodiment or description of the Prior Art be briefly described below, apparently, the accompanying drawing the following describes is only some embodiment that record in the present invention, for those of ordinary skills, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing.
Fig. 1 is towards the process flow diagram of the numerical control processing track disposal route of fairing processing in the embodiment of the invention;
Fig. 2 is the particular flow sheet of step S1 interpolation sub-range decision method in first embodiment of the invention;
Fig. 3 is the particular flow sheet of step S2 interpolation calculation process in first embodiment of the invention;
Fig. 4 is towards the process flow diagram of the numerical control processing track disposal route of fairing processing in the present invention's two embodiments;
Fig. 5 is the particular flow sheet of step S3 fairing filtering sub-range decision method in second embodiment of the invention;
Fig. 6 is the particular flow sheet of step S4 fairing filtering in second embodiment of the invention;
Fig. 7 is the schematic diagram of two kinds of possibilities of circular arc direction, wherein, and the schematic diagram that Fig. 7 (a) is upper circular arc, the schematic diagram that Fig. 7 (b) is lower circular arc;
Fig. 8 is for calculating the boost line schematic diagram of interpolation circular arc expression formula;
Fig. 9 for interpolation calculation on circular arc, obtain the schematic diagram of interpolation point;
Figure 10 is the module diagram of moving average filter.
Embodiment
In order to make those skilled in the art person understand better the technical scheme in the present invention, below in conjunction with the accompanying drawing in the embodiment of the present invention, technical scheme in the embodiment of the present invention is clearly and completely described, obviously, described embodiment is only the present invention's part embodiment, rather than whole embodiment.Embodiment based in the present invention, those of ordinary skills, not making the every other embodiment obtaining under creative work prerequisite, should belong to the scope of protection of the invention.
In order to solve the existing deficiency to fairing working research, in the factors of the above-mentioned impact that fairing processing is caused, the present invention will consider emphatically that wall scroll machining path does not meet this problem of fairing processing conditions, the fairing problem of pretreatment of research Machining Path, provides a kind of numerical control movement locus disposal route towards fairing processing.
Shown in ginseng Fig. 1, in first embodiment of the invention, the numerical control processing track disposal route of processing towards fairing comprises the following steps:
All little line segment on S1, traversal whole piece machining locus, carries out the judgement in interpolation sub-range;
S2, to the little line segment in interpolation sub-range, adopt the method for circular interpolation to carry out interpolation calculation.
First the method that a kind of interpolation sub-range embodiment of the present invention step S1 being provided is below judged is introduced.
When processing adopts the represented machining locus of nurbs curve, there is the variation of machine direction in each interpolation cycle, and this has just comparatively been evenly distributed in the turning angle of each flex point in the represented reinforcing track of little line segment in a plurality of interpolation cycles.Thereby nurbs curve interpolation technique has higher process velocity, precision and better finished surface fairness.
According to These characteristics, in order to make the represented machining locus of little line segment can be suitable for better the demand of fairing processing, the present invention adopts circular interpolation technology, by satisfactory one section little line segment interpolation, it is the little line segment of multistage, thereby the angle of former flex point is changed and shared comparatively equably in a plurality of flex points, make finished surface there is better fairness.
Designed interpolation calculation algorithm is in order to reduce the low-angle flex point transition on machining locus, need to carry out interpolation arithmetic, and joined in the middle of interpolation sub-range so which little line segment is algorithm first need to judge.
Shown in ginseng Fig. 2, step S1 specifically comprises:
Little line segment on S11, traversal whole piece machining locus;
S12, the little line segment length of the shortest interpolation of setting;
S13, judge that whether current traversed little line segment length is greater than the little line segment length of the shortest interpolation setting, and if so, carries out S14; Otherwise, carry out S18;
S14, set maximum turning;
S15, judge that whether the turning size of little line segment destination county is less than the maximum turning setting, and if so, carries out S16; Otherwise, carry out S18;
S16, this little line segment is joined in interpolation sub-range;
S17, obtain needing the little line segment aggregate of interpolation calculation;
S18, obtain not needing the little line segment aggregate of interpolation calculation.
The process of the interpolation calculation below embodiment of the present invention step S2 being provided is introduced.
For all little line segments that join in interpolation sub-range, adopt the method for circular interpolation to carry out interpolation calculation to it.Obviously, if the little line segment obtaining after interpolation is too short, may makes the little line segment length after interpolation be less than the actual actual step size that adds each interpolation cycle in man-hour, thereby affect working (machining) efficiency.For fear of this situation, occur, set the minimum step of an interpolation, the little line segment length obtaining after interpolation should not be less than this minimum step, minimum step L after the interpolation of supposing to allow
minrepresent.
Shown in ginseng Fig. 3, step S2 specifically comprises:
S21, obtain the little line segment in interpolation sub-range;
Here given little line segment is after interpolation sub-range is judged, needs any one section of little line segment in set that difference calculates.
S22, with one section of circular arc, approach original little line segment;
The direction of S23, judgement circular arc;
In order to guarantee to guarantee as much as possible machining precision when approaching little line segment with circular arc, wish that the direction of circular arc is identical with the direction of a curve on original processing curve.Track generating principle and observation by CAM are found, by the tracing point adjacent with little line segment, can obtain and make circular arc closer to the interpolation circular arc direction of original processing curve.Meanwhile, if upwards build circular arc the party, not only can not lose machining precision, the part precision of losing while also CAM being generated to machining locus has compensating action.
As shown in Figure 7, get two terminal A and the B of this little line segment, and next tracing point C of terminal B, take A as true origin, line segment AB direction is X-direction, if some C above X-axis, interpolation circular arc should be lower circular arc, shown in ginseng Fig. 7 (b); Otherwise some C is below X-axis, interpolation circular arc is upper circular arc, shown in ginseng Fig. 7 (a).
S24, obtain the expression formula of circular arc;
Suppose that maximum mismachining tolerance is ε, next just can, according to two end points coordinates of the direction of circular arc, maximum mismachining tolerance ε and the little line segment of interpolation, obtain the expression formula of this circular arc.When the direction of circular arc is known, the expression formula of this circular arc is by two end points of circular arc and arc radius is unique determines.In desired interpolation circular arc, two end points of circular arc are two end points of the little line segment of wanted interpolation.So only a bit on circular arc need to be obtained again, according to formula (1), just the expression formula of this circular arc can be obtained.
（x-a)
2+(y-b)
2＝R
2 （1）
S25, obtain the expression formula of interpolation circular arc;
As shown in Figure 8, little line segment AB can be regarded as the string of circular arc place circle, gets the mid point of AB, and note is an O, then from O point, does the vertical line of AB, and note is OE.Then line taking section OF on OE, makes the length of OF equal maximum mismachining tolerance, bends high level error ε.Finally, obtain the coordinate figure of a F.Like this, certainly exist a circle, cross A, F, B 3 points simultaneously.According to formula (1), can obtain parameter a, b, the concrete value of R, thus obtain the expression formula of this interpolation circular arc.
S26, at the enterprising row interpolation of circular arc, calculate, obtain interpolation point.
When interpolation calculation, utilize previously defined interpolation after minimum step remove to approach this interpolation circular arc, specific practice is as follows:
From circular arc starting point (former little line segment starting point), with minimum interpolation step-length L
minas chord length, remove to approach interpolation circular arc.Suppose that circular arc starting point is A, as shown in Figure 9, first interpolation point obtaining after interpolation is B, and their coordinate is used respectively (x
a, y
a) and (x
b, y
b) represent.Obviously, B is a bit on circular arc, and the distance of ordering to A is L
min.Basis formula (2) below, can be easy to obtain the coordinate figure that B is ordered so.
Next, the interpolation point below B point starts to continue to solve according to the method described above, till to the last an interpolation point coordinate exceeds the scope of circular arc.
If the distance dropping on the interpolation point in circular arc to last from circular arc terminal is less than minimum interpolation step-length, last interpolation point before circular arc terminal is deleted, and using circular arc terminal as last interpolation point.
For fear of the interpolation point generating after interpolation redundancy too, algorithm also needs to set a maximum turning θ
maxif the angle between two sections of new little line segments that generate after interpolation is greater than maximum turning θ
max, two interpolation points are merged into an interpolation point, the starting point of the little line segment of first paragraph of take is new starting point, the terminal of the little line segment of second segment of take is terminal.
Shown in ginseng Fig. 4, in second embodiment of the invention, the numerical control processing track disposal route of processing towards fairing comprises the following steps:
All little line segment on S1, traversal whole piece machining locus, carries out the judgement in interpolation sub-range;
S2, to the little line segment in interpolation sub-range, adopt the method for circular interpolation to carry out interpolation calculation;
All little line segment on S3, traversal whole piece machining locus, carries out the judgement in fairing filtering sub-range;
S4, to carrying out each turning of fairing filtering, adopt glide filter technology to carry out filtering.
Wherein step S1 is identical with the first embodiment with S2, at this, no longer repeats.In order to obtain the machining locus of more fairing, the transition energy even variation of angle between flex point on machining locus.Therefore, after completing interpolation, also need to travel through whole piece machining locus, carry out the judgement in fairing filtering sub-range, then to carrying out each turning of fairing filtering, adopt glide filter technology to carry out filtering, thereby the variation of angle between flex point can not undergone mutation.
The method that the fairing filtering sub-range below embodiment of the present invention step S3 being provided is judged is introduced.
The interpolation technique of little line segment is mainly applicable to exist little flex point and the longer situation of the little line segment of wall scroll.In order to obtain the machining locus of more fairing, also wish on machining locus the transition energy even variation of angle between flex point.Therefore, after completing interpolation, also need to travel through whole piece machining locus, to each turning on track, adopt glide filter technology to carry out filtering, thereby the variation of angle between flex point can not undergone mutation.
Digital control system is a real-time system, and obviously, if whole piece curve is all carried out to filtering, to process the spent time longer, is difficult to the real-time of assurance system.And, angle is carried out to filtering meeting the shape of track is brought to certain impact, might not be adapted to whole piece Processing Curve.Therefore,, before machining locus is carried out to fairing filtering, first designed algorithm need to find the sub-range that needs fairing filtering on whole piece machining locus.
Shown in ginseng Fig. 5, step S3 is specially:
S31, travel through the tracing point on every paths;
S32, according to direction between little line segment, change and should meet conforming principle whole piece machining locus is divided into several sub-ranges;
The principle of glide filter technology is that the value within the scope of current glide filter is changed comparatively equably, therefore, when the turning in track (direction of namely little line segment changes) carries out filtering, can change to a certain extent the shape of original machining locus.Particularly within the scope of glide filter, the direction of little line segment changes when inconsistent, even occurs the shape errors that filtering causes.Therefore, only the direction between little line segment being changed to consistent sub-range adopts sliding filter to carry out fairing filtering.
S33, judge in sub-range whether at least exist two turnings between adjacent little line segment to be less than preset value, if so, to carry out S34; Otherwise, carry out S35;
S34, obtain needing the set in the sub-range of fairing filtering;
S35, obtain not needing the set in the sub-range of fairing filtering.
Fairing filtering algorithm will carry out fairing filtering to meet the machining locus sub-range of above two conditions simultaneously.Be implemented as follows:
The Y-axis coordinate of the little line segment starting point little line segment larger than terminal is defined as to the little line segment that declines; Otherwise, be defined as the little line segment that rises.Traversal whole piece machining locus, all little line segments are classified according to above-mentioned definition, and the little line segment that type is changed is just defined as the beginning or end in a track sub-range.Whole piece machining locus is just divided for several sub-ranges like this, and in each sub-range, the direction of little line segment changes consistent.Meanwhile, the maximum turning of definition filtering is θ
max, when traversal machining locus, find all turnings to be less than θ
maxall flex points, and be marked.
Travel through all sub-ranges, if exist at least one turning to be less than θ in current traveled through sub-range
maxflex point, this sub-range needs fairing filtering, is added fairing filtering buffer zone; Otherwise current sub-range does not need fairing filtering.
For the sub-range that needs fairing filtering, also need further to revise the size in sub-range, to guarantee that original machining locus is not produced to excessive impact.Because the direction of little line segment in sub-range changes unanimously, therefore can change according to the direction of the little line segment of head-end sections in sub-range, obtain the size at average each turning after glide filter.If judge the maximum turning θ that is greater than defined filtering at average each turning, current sub-range
max, sub-range is located from beginning to end to delete apart from the little flex point of mark one section little line segment relatively far away, shorten the size in sub-range.Then adopt said method to continue judge and shorten sub-range, until the size at average each turning is less than maximum turning θ after filtering
maxtime till.The sub-range now obtaining is exactly real filtering sub-range.
The process of the fairing filtering below embodiment of the present invention step S4 being provided is introduced.
What fairing filtering algorithm adopted is moving average filter, and its structural drawing as shown in figure 10.
Shown in ginseng Fig. 6, step S4 is specially:
S41, moving window N is set
w;
The glide filter that defines this sliding filter is interval, i.e. the size of moving window.
S42, obtain the result output of this cycle glide filter;
Each glide filter is first values all in moving window to be sued for peace, and then divided by moving window size, obtains the average of all values, as the result output of this cycle glide filter.
Need to from the beginning travel through each section little line segment in filtering sub-range.Be not general, for the little line segment of i bar on filtering sub-range, its fairing wave filter is output as:
S43, to the variation of little line segment angle, adopt moving average filter to carry out filtering.
Suppose the total little line segment of N bar, the so N in above formula on this filtering sub-range
jshould meet following formula:
N
j＝min(i+N
w,N)，
Keep length and the starting point coordinate of the little line segment of i bar constant, by the output of fairing wave filter, can calculate the terminal point coordinate of this little line segment.Then the starting point using tried to achieve terminal as next little line segment, continues to adopt said method to process next little line segment, until whole filtering sub-range is all processed complete.
Compared with prior art, numerical control processing track disposal route towards fairing processing of the present invention, glide filter technology and interpolation technique are incorporated in the fairing processing problem of Machining Path, at the machining path little line segment not being formed, fit on the basis of curve, design a kind of pre-service mechanism in continually varying fairing path, turning between adjacent little line segment that realizes on machining path.For the machining locus with different characteristics, adopt different preprocess methods.For example, for the longer machining locus of the little line segment of wall scroll, adopt the mode of interpolation, and for the shorter machining locus of the little line segment of wall scroll, further adopt the mode of glide filter to reduce low-angle tracing point transition, meet the requirement of digital control system real-time, strengthen the adaptability of fairing processing function.
To those skilled in the art, obviously the invention is not restricted to the details of above-mentioned one exemplary embodiment, and in the situation that not deviating from spirit of the present invention or essential characteristic, can realize the present invention with other concrete form.Therefore, no matter from which point, all should regard embodiment as exemplary, and be nonrestrictive, scope of the present invention is limited by claims rather than above-mentioned explanation, is therefore intended to include in the present invention dropping on the implication that is equal to important document of claim and all changes in scope.Any Reference numeral in claim should be considered as limiting related claim.
In addition, be to be understood that, although this instructions is described according to embodiment, but not each embodiment only comprises an independently technical scheme, this narrating mode of instructions is only for clarity sake, those skilled in the art should make instructions as a whole, and the technical scheme in each embodiment also can, through appropriately combined, form other embodiments that it will be appreciated by those skilled in the art that.
Claims (7)
1. towards a numerical control processing track disposal route for fairing processing, it is characterized in that, said method comprising the steps of:
All little line segment on S1, traversal whole piece machining locus, carries out the judgement in interpolation sub-range;
S2, to the little line segment in interpolation sub-range, adopt the method for circular interpolation to carry out interpolation calculation.
2. method according to claim 1, is characterized in that, described step S1 specifically comprises:
Little line segment on S11, traversal whole piece machining locus;
S12, the little line segment length of the shortest interpolation of setting;
S13, judge that whether current traversed little line segment length is greater than the little line segment length of the shortest interpolation setting, and if so, carries out S14; Otherwise, carry out S18;
S14, set maximum turning;
S15, judge that whether the turning size of little line segment destination county is less than the maximum turning setting, and if so, carries out S16; Otherwise, carry out S18;
S16, this little line segment is joined in interpolation sub-range;
S17, obtain needing the little line segment aggregate of interpolation calculation;
S18, obtain not needing the little line segment aggregate of interpolation calculation.
3. method according to claim 1, is characterized in that, described step S2 specifically comprises:
S21, obtain the little line segment in interpolation sub-range;
S22, with one section of circular arc, approach original little line segment;
The direction of S23, judgement circular arc;
S24, obtain the expression formula of circular arc;
S25, obtain the expression formula of interpolation circular arc;
S26, at the enterprising row interpolation of circular arc, calculate, obtain interpolation point.
4. method according to claim 1, is characterized in that, after described step S2, also comprises:
All little line segment on S3, traversal whole piece machining locus, carries out the judgement in fairing filtering sub-range;
S4, to carrying out each turning of fairing filtering, adopt glide filter technology to carry out filtering.
5. method according to claim 4, is characterized in that, described step S3 is specially:
S31, travel through the tracing point on every paths;
S32, according to direction between little line segment, change and should meet conforming principle whole piece machining locus is divided into several sub-ranges;
S33, judge in sub-range whether at least exist two turnings between adjacent little line segment to be less than preset value, if so, to carry out S34; Otherwise, carry out S35;
S34, obtain needing the set in the sub-range of fairing filtering;
S35, obtain not needing the set in the sub-range of fairing filtering.
6. method according to claim 5, is characterized in that, described step S4 is specially:
S41, moving window N is set
w;
S42, obtain the result output of this cycle glide filter;
S43, to the variation of little line segment angle, adopt moving average filter to carry out filtering.
7. method according to claim 6, is characterized in that, in described step S42, for the little line segment of i bar on filtering sub-range, Output rusults is:
and N
jmeet N
j=mini (+N
wn,, wherein, the number that N is little line segment.
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| CN104875104A (en) * | 2015-05-14 | 2015-09-02 | 常州大思世成机电科技有限公司 | Wheel hub irregular curved surface polishing method based on CAD/CAM technologies |
| CN107247446A (en) * | 2017-06-29 | 2017-10-13 | 深圳市雷赛控制技术有限公司 | Special-shaped track control method and device |
| CN108062073A (en) * | 2016-11-08 | 2018-05-22 | 沈阳高精数控智能技术股份有限公司 | A kind of circular arc smooth compression interpolation algorithm for high quality processing |
| CN110531700A (en) * | 2019-09-09 | 2019-12-03 | 西北工业大学 | Space corner method for fairing based on Three Dimensional Generalized Euler's helical |
| CN112506139A (en) * | 2020-11-23 | 2021-03-16 | 西北工业大学 | Partial corner fairing method for five-axis short straight line segment track |
| CN112859750A (en) * | 2019-11-27 | 2021-05-28 | 西安交通大学 | Processing track local fairing method for geometric fairing and speed planning synchronous design |
| CN116009473A (en) * | 2022-10-25 | 2023-04-25 | 华中科技大学 | Tool pose track interpolation and fairing method based on asymmetric FIR filter |
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