CN105137914A - Three-point circle method parameter self-adaptive interpolation algorithm applied to numerical control machine tool - Google Patents
Three-point circle method parameter self-adaptive interpolation algorithm applied to numerical control machine tool Download PDFInfo
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- CN105137914A CN105137914A CN201510401156.5A CN201510401156A CN105137914A CN 105137914 A CN105137914 A CN 105137914A CN 201510401156 A CN201510401156 A CN 201510401156A CN 105137914 A CN105137914 A CN 105137914A
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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Abstract
The invention relates to a three-point circle method parameter self-adaptive interpolation algorithm applied to a numerical control machine tool. The three-point circle method parameter self-adaptive interpolation algorithm comprises the steps of: expressing a non-circle curve equation with parameter formulas, and ensuring that each parameter is corresponding to each function value; successively getting three points D, E and F on the curve in an isoparametric manner; calculating coordinates of a circle center point of an arc passing the three points and the radius R of the arc; then deriving a discriminant for determining whether the arc is clockwise or anticlockwise, and determining whether arc interpolation at this time is clockwise or anticlockwise; finding an intermediate point H between the D point and the E point, calculating the distance [Rho]1 from the point H to the circle center, and similarly, finding an intermediate point I between the E point and the F point, and calculating the distance [Rho]2 from the point H to the circle center; respectively calculating [delta]1 and [delta]2, wherein [delta]1=absolute([Rho]1-R), [delta]2=absolute([Rho]2-R), and [delta]1 and [delta]2 are used as interpolation errors; and comparing [delta]1 and [delta]2 with an allowable error [delta]<allowable>. The three-point circle method parameter self-adaptive interpolation algorithm has the advantages that the interpolation calculation is simplified, the solving process is simple, the solving difficulty is small, the interpolation quality and efficiency are improved, etc.
Description
Technical field
The invention belongs to numerical control machine tool technique field, relate to a kind of 3 circule method parameter adaptive interpolation algorithms being applied to numerically-controlled machine.
Background technology
Interpolation is the core in Numeric Control Technology; it can according to the overall size of part; in conjunction with the requirement of the aspect such as precision and technique; some intermediate points are determined according between the known point of certain mathematical method on desirable track or profile; thus approaching desirable workpiece configurations profile, interpolation is also referred to as " densification of data point ".
Interpolation algorithm will solve two problems, and one is node selection, namely carries out getting a little on curve according to what rule and condition; Two is interpolation modes of adjacent node, namely carries out what kind of moving interpolation between adjacent node.Mode is chosen for interpolator node, the parameters such as general employing, equal error, etc. three kinds of modes such as chord length carry out.A convenience is simply got in calculating Deng parameter interpolation, but the quantity of getting a little can be a lot; Equal error method well can control the error of interpolation in each place, reduce the quantity of interpolated point, but this method relates to solving of biquadratic equation, and its calculated amount is very large, and solution procedure is complicated; Time larger for the Curvature varying of interpolation curve etc. this interpolation mode of chord length, larger error of interpolation can be produced.Above-mentioned three kinds of interpolating methods respectively have relative merits, if three kinds of interpolation point sampling methods can be combined, can meet interpolation algorithm error, can reduce calculated amount again, this is also the direction that we will study.
Common numerically-controlled machine possesses straight line and circular interpolation function, for non-circular curve, traditional interpolation mode adopts linear interpolation by between the adjacent node chosen, namely adjacent point-to-point transmission adopts small straight-line segment to connect, when the quantity of node obtains abundant, the profile connect some sections of broken lines and the actual profile of curve are closely, this interpolating method calculates simple, interpolation is convenient, but with regard to interpolation quality with to regard to the control of lathe, it is harmful that broken line connects for interpolation quality and interpolation speed of feed.Compared with linear interpolation mode, circular interpolation has more advantage, connects between adjacent node with circular arc, and the surface of processing can smoothly transit by circular arc, and the quality of processing is high, processing effective.
Summary of the invention
For overcoming above-mentioned technical disadvantages, the invention provides a kind of 3 circule method parameter adaptive interpolation algorithms being applied to numerically-controlled machine, it using parameter intermediate point to the difference between the distance in the center of circle and center of circle radius as error of interpolation, parameter is adjusted by controlling interpolation maximum error value, realize parameter adaptive, its computation process is simpler than traditional equal error method, and its interpolation precision is higher than traditional Isoparametric method; Substitute 2 traditional alignments with three-point circle, substitute linear interpolation with circular interpolation, decrease interpolator node, improve interpolation quality and Product Precision; Utilized by this technology law macroprogram on HTC32100am turning center, realize turning and the milling of non-circular curve respectively, this interpolation technique is verified, solve a circular interpolation difficult problem for non-circular curve.
The present invention solves the technical method that its technical matters adopts: a kind of 3 circule method parameter adaptive interpolation algorithms being applied to numerically-controlled machine, and its step is as follows:
The first step, expresses the equation parameter type of non-circular curve, guarantees often to get the corresponding functional value of a parameter;
Second step, gets three somes D, E, F successively by isoparametric mode on curve, guarantees that three points are on same curves;
3rd step, calculates the centre point coordinate of circular arc by 3 and the radius R of circular arc;
4th step, derives circular arc along inverse discriminant, judges the suitable inverse of this circular interpolation;
5th step, finds out the parameter intermediate point H of D point and E point, and calculates the distance of H point to the center of circle
, in like manner find out the parameter intermediate point I of E point and F point, and calculate the distance of I point to the center of circle
;
6th step, calculates respectively
with
, wherein
,
, and will
with
as error of interpolation;
7th step, compares
with
with interpolation permissible error
size, have four kinds may, if
with
all be less than or equal to
namely meet error of interpolation condition, directly can carry out circular interpolation; If
with
all be greater than
, then get D, H, E at 3 and re-start calculating as new interpolated point, when meeting error of interpolation condition, carry out circular interpolation, then again get parameter intermediate point when not meeting and calculate; If
be greater than
and
be less than or equal to
, then get D, H, I at 3 and re-start calculating as new interpolated point, carry out circular interpolation when meeting error of interpolation condition, otherwise again get parameter intermediate point; If
be less than or equal to
and
be greater than
, then get D, E, I at 3 and re-start calculating as new interpolated point, carry out circular interpolation when meeting error of interpolation condition, otherwise again get parameter intermediate point;
8th step, using the starting point of the terminal of a upper interpolation as next interpolation, chooses 2 points successively more again by isoparametric mode, carries out interpolation calculating, circulate according to this, until interpolation terminates to this three step pressed above.
The invention has the beneficial effects as follows: one is solve interpolator node choosing method when non-circular curve carries out interpolation, the circular interpolation of non-circular curve optimizes the calculating of error with parameter intermediate point, carrying out regulating parameter by controlling maximum error of interpolation, realizing the self-adaptation of parameter; Two is the correlation computations solving circular interpolation, by adjacent three points, obtains the center of circle and radius, and derives circular arc along inverse discriminant by the position relationship of 3 on the center of circle and circular arc, and the circular arc of judgement along inverse, thus carries out circular interpolation; Three is solve the conversion that interpolation calculates thinking and macroprogram, is expressed by the thinking algorithm flow chart of interpolation calculating, and uses the macroprogram language that lathe can understand and write, and circular interpolation lathe carrying out non-circular curve is achieved; Four is the embody rule solving technology, in conjunction with the product (LED lamp reflector parabolic curve and elliptic curve) of real enterprise non-circular curve, on the horizontal turning center of concrete HTC32100am, carry out the checking of numerical control turning and numerical control milling, the correctness of this technology is verified with real effect, have simplify interpolation calculating, solution procedure is simple, solve difficulty little, improve the features such as interpolation quality and efficiency.
Accompanying drawing explanation
Fig. 1 is present invention process process flow diagram.
Embodiment
Below in conjunction with embodiment, the present invention is further described.
See Fig. 1, a kind of 3 circule method parameter adaptive interpolation algorithms being applied to numerically-controlled machine, its step is as follows:
The first step, expresses the equation parameter type of non-circular curve, guarantees often to get the corresponding functional value of a parameter;
Second step, gets three somes D, E, F successively by isoparametric mode on curve, guarantees that three points are on same curves;
3rd step, calculates the centre point coordinate of circular arc by 3 and the radius R of circular arc;
4th step, derives circular arc along inverse discriminant, judges the suitable inverse of this circular interpolation;
5th step, finds out the parameter intermediate point H of D point and E point, and calculates the distance of H point to the center of circle
, in like manner find out the parameter intermediate point I of E point and F point, and calculate the distance of I point to the center of circle
;
6th step, calculates respectively
with
, wherein
,
, and will
with
as error of interpolation;
7th step, compares
with
with interpolation permissible error
size, have four kinds may, if
with
all be less than or equal to
namely meet error of interpolation condition, directly can carry out circular interpolation; If
with
all be greater than
, then get D, H, E at 3 and re-start calculating as new interpolated point, when meeting error of interpolation condition, carry out circular interpolation, then again get parameter intermediate point when not meeting and calculate; If
be greater than
and
be less than or equal to
, then get D, H, I at 3 and re-start calculating as new interpolated point, carry out circular interpolation when meeting error of interpolation condition, otherwise again get parameter intermediate point; If
be less than or equal to
and
be greater than
, then get D, E, I at 3 and re-start calculating as new interpolated point, carry out circular interpolation when meeting error of interpolation condition, otherwise again get parameter intermediate point;
8th step, using the starting point of the terminal of a upper interpolation as next interpolation, chooses 2 points successively more again by isoparametric mode, carries out interpolation calculating, circulate according to this, until interpolation terminates to this three step pressed above.
Embodiment 1:
When the parameter such as pressing
mode gets three somes D, E, F on curve,
, then the coordinate of 3 is known, is respectively D(
,
), E(
,
), F(
,
), then by the coordinate of the centre point C of three null circles (
,
) for asking, radius of a circle R, also for asking, gets the parameter intermediate point H of D, E 2, and get the parameter intermediate point I of E, F, then H point to parameter is just
, I point to parameter is just
, the coordinate of its H, I point is respectively H(
,
), I(
,
), be known, then can obtain the distance of H point to center of circle C
, I point is to the distance of center of circle C
; Calculate
with the difference of arc radius R
,
with the difference of arc radius R
, and it can be used as error of interpolation.
Relatively
,
with the size of permissible error value, when
with
when being all less than or equal to permissible error value, direct D, E, F 3 of crossing makes circular interpolation; When
with
when being all greater than permissible error value, getting D, H, E at 3 and recalculate error of interpolation; When
be less than or equal to permissible error and
when being greater than permissible error value, getting D, E, I at 3 and recalculate error of interpolation; When
be greater than permissible error and
when being less than or equal to permissible error value, getting D, H, I at 3 and recalculate error of interpolation; Till meeting error permissive condition.
According to the algorithm provided, the programming feature of combined techniques FANUC digital control system writes macroprogram order format.Assignment statement will be used, loop statement (WHILE) and skip instruction (GOTO) in whole macro programming;
Algorithm is used on the curve such as ellipse, para-curve, according to the canonical form of elliptic equation equation
, become parametric form instead
,
, will
tas interpolation parameters, concrete macroprogram of programming, in like manner, writes concrete macroprogram according to parabolical equation;
Utilize turning center to carry out concrete cutting checking, turning centre not only can carry out turnery processing, also can carry out Milling Process simultaneously, and the precision of processing is high.This algorithm is really carried out Product processing on lathe, is come correctness and the high efficiency of verification algorithm by the crudy of testing product.
The present invention one solves interpolator node choosing method when non-circular curve carries out interpolation, and the circular interpolation of non-circular curve optimizes the calculating of error with parameter intermediate point, carrying out regulating parameter, realizing the self-adaptation of parameter by controlling maximum error of interpolation; Two is the correlation computations solving circular interpolation, by adjacent three points, obtains the center of circle and radius, and derives circular arc along inverse discriminant by the position relationship of 3 on the center of circle and circular arc, and the circular arc of judgement along inverse, thus carries out circular interpolation; Three is solve the conversion that interpolation calculates thinking and macroprogram, is expressed by the thinking algorithm flow chart of interpolation calculating, and uses the macroprogram language that lathe can understand and write, and circular interpolation lathe carrying out non-circular curve is achieved; Four is the embody rule solving technology, in conjunction with the product (LED lamp reflector parabolic curve and elliptic curve) of real enterprise non-circular curve, on the horizontal turning center of concrete HTC32100am, carry out the checking of numerical control turning and numerical control milling, the correctness of this technology is verified with real effect, have simplify interpolation calculating, solution procedure is simple, solve difficulty little, improve the features such as interpolation quality and efficiency.
Claims (1)
1. be applied to 3 circule method parameter adaptive interpolation algorithms of numerically-controlled machine, it is characterized in that step is as follows:
The first step, expresses the equation parameter type of non-circular curve, guarantees often to get the corresponding functional value of a parameter;
Second step, gets three somes D, E, F successively by isoparametric mode on curve, guarantees that three points are on same curves;
3rd step, calculates the centre point coordinate of circular arc by 3 and the radius R of circular arc;
4th step, derives circular arc along inverse discriminant, judges the suitable inverse of this circular interpolation;
5th step, finds out the parameter intermediate point H of D point and E point, and calculates the distance of H point to the center of circle
, in like manner find out the parameter intermediate point I of E point and F point, and calculate the distance of I point to the center of circle
;
6th step, calculates respectively
with
, wherein
,
, and will
with
as error of interpolation;
7th step, compares
with
with interpolation permissible error
size, have four kinds may, if
with
all be less than or equal to
namely meet error of interpolation condition, directly can carry out circular interpolation; If
with
all be greater than
, then get D, H, E at 3 and re-start calculating as new interpolated point, when meeting error of interpolation condition, carry out circular interpolation, then again get parameter intermediate point when not meeting and calculate; If
be greater than
and
be less than or equal to
, then get D, H, I at 3 and re-start calculating as new interpolated point, carry out circular interpolation when meeting error of interpolation condition, otherwise again get parameter intermediate point; If
be less than or equal to
and
be greater than
, then get D, E, I at 3 and re-start calculating as new interpolated point, carry out circular interpolation when meeting error of interpolation condition, otherwise again get parameter intermediate point;
8th step, using the starting point of the terminal of a upper interpolation as next interpolation, chooses 2 points successively more again by isoparametric mode, carries out interpolation calculating, circulate according to this, until interpolation terminates to this three step pressed above.
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|---|---|---|---|
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113791581A (en) * | 2021-08-03 | 2021-12-14 | 天津中德应用技术大学 | Spherical shrub spherical interpolation algorithm based on equal-chord segmentation sampling |
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| EP0618522A1 (en) * | 1992-10-09 | 1994-10-05 | Fanuc Ltd. | Numerically controlled apparatus |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113791581A (en) * | 2021-08-03 | 2021-12-14 | 天津中德应用技术大学 | Spherical shrub spherical interpolation algorithm based on equal-chord segmentation sampling |
| CN113791581B (en) * | 2021-08-03 | 2023-08-08 | 天津中德应用技术大学 | Spherical shrub sphere interpolation algorithm based on equal chord division sampling |
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