CN116679622A - Surface shape tool mark error prediction method based on continuous tool function - Google Patents

Surface shape tool mark error prediction method based on continuous tool function Download PDF

Info

Publication number
CN116679622A
CN116679622A CN202310967454.5A CN202310967454A CN116679622A CN 116679622 A CN116679622 A CN 116679622A CN 202310967454 A CN202310967454 A CN 202310967454A CN 116679622 A CN116679622 A CN 116679622A
Authority
CN
China
Prior art keywords
tool
point
surface shape
function
residence time
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202310967454.5A
Other languages
Chinese (zh)
Other versions
CN116679622B (en
Inventor
李龙响
刘夕铭
李兴昶
张峰
张学军
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Changchun Institute of Optics Fine Mechanics and Physics of CAS
Original Assignee
Changchun Institute of Optics Fine Mechanics and Physics of CAS
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Changchun Institute of Optics Fine Mechanics and Physics of CAS filed Critical Changchun Institute of Optics Fine Mechanics and Physics of CAS
Priority to CN202310967454.5A priority Critical patent/CN116679622B/en
Publication of CN116679622A publication Critical patent/CN116679622A/en
Application granted granted Critical
Publication of CN116679622B publication Critical patent/CN116679622B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • 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
    • G05B19/416—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 of velocity, acceleration or deceleration
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/32—Operator till task planning
    • G05B2219/32063—Adapt speed of tool as function of deviation from target rate of workpieces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Algebra (AREA)
  • Pure & Applied Mathematics (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Automation & Control Theory (AREA)
  • Numerical Control (AREA)

Abstract

The invention relates to the technical field of optical machining surface shape prediction, in particular to a surface shape tool mark error prediction method based on a continuous tool function, which comprises the following steps: s1, measuring the surface shape of a workpiece to be processed through an interferometer to obtain discretized removal quantity distribution of the workpiece to be processed; s2, selecting a machining mode of a workpiece to be machined, and measuring a tool influence function; s3, designing a machining track according to the size of the workpiece to be machined; s4, calculating residence time distribution of the cutter according to the machining track, the removal amount distribution and the tool influence function; s5, calculating a continuous tool function between any two adjacent points on the processing track based on residence time distribution of the cutter; s6, carrying out dimension expansion on all continuous tool functions to the full caliber of the workpiece to be processed, adding, and predicting the surface shape tool mark error of the workpiece to be processed. The invention can refine the global cutter removal characteristic, embody the cutter mark generated by cutter feeding and improve the prediction capability of the optical processing surface shape.

Description

Surface shape tool mark error prediction method based on continuous tool function
Technical Field
The invention relates to the technical field of optical machining surface shape prediction, in particular to a surface shape tool mark error prediction method based on a continuous tool function.
Background
The existing surface shape prediction standard of the optical element after processing is that in the step of calculating the residence time, the convolution of the function and the residence time is influenced by a surface shape residual error subtracting tool, and the convergence rate is defined by adopting RMS before and after processingEvaluation was performed. The closer the convergence rate is to 100%, the better the surface shape convergence is said to be.
However, some deviation exists between the machined surface calculated by the model and the actual machined surface, for example, the intermediate frequency error of the tool mark (ToolMask) type left after machining by a machine tool can not be calculated by the existing surface shape prediction algorithm.
The Chinese patent publication number is CN111906596A, the publication date is 11 months and 10 days in 2020, and the patent name is an electroencephalogram signal classification method based on model uncertainty learning. The paper with the name of [ Key technology research on magnetorheological finishing based on suppression of surface mid-spatial frequency ripple errors ] published by the national defence and science and technology university of Chinese people also obtains the equivalent conclusion through a large amount of calculation.
However, in most cases, or in isotropic tool-influencing function processing, the concept of magic angles does not exist or is weak. However, if only a trace exists, a tool mark is generated. The presence of the tool marks has a direct effect on the decision and imaging of the optical processing procedure, so that the tool marks after processing must be estimated.
The paper published by Jilin university under the name [ Analytical and stochastic modeling of surface topography in time-dependent sub-aperture processing ] states that the tool mark is analytically expressed by fitting a tool influence function with Gauss, but the tool influence function for MRF [ magnetorheological processing ] is an asymmetrical tool influence function of bullet type ] and the tool influence function for EMM [ elastic emission processing ] is a horseshoe type ], without a near-fitting tool influence function.
In summary, in the technical field of optical processing surface shape prediction, there is no method capable of predicting a tool mark error after actual processing.
Disclosure of Invention
In view of the above, the invention provides a surface shape tool mark error prediction method based on a continuous tool function, which solves the problem that the tool mark error cannot be predicted in the conventional surface shape prediction process, and further improves the surface shape prediction capability of optical processing.
The invention provides a surface shape tool mark error prediction method based on a continuous tool function, which comprises the following steps:
s1, measuring the surface shape of a workpiece to be processed through an interferometer to obtain discretized removal quantity distribution of the workpiece to be processed;
s2, selecting a machining mode of a workpiece to be machined, and measuring a tool influence function;
s3, designing a machining track according to the size of the workpiece to be machined;
s4, calculating residence time distribution of the cutter according to the machining track, the removal amount distribution and the tool influence function;
s5, calculating a continuous tool function between any two adjacent points on the processing track based on residence time distribution of the cutter;
s6, carrying out dimension expansion on all continuous tool functions to the full caliber of the workpiece to be processed, adding, and predicting the surface shape tool mark error of the workpiece to be processed.
Preferably, step S5 specifically includes the following steps:
s51, discretizing a processing track into a limited resident point, arbitrarily selecting two adjacent resident points, marking the two adjacent resident points as a point A and a point B, and inserting sub-resident points between the point A and the point B for a tool influence function to carry out convolution operation; the relationship between the number of inserted sub-dwell points and the sampling interval of the tool-impact function is as follows:
；
wherein ,representing the number of inserted sub-dwell points, s representing the feed amount, EDG representing the variable dimension expansion interval, +.>Represents any integer, +.>Representing a positive integer set;
s52, calculating residence time nodes for distributing sub-residence points between the point A and the point B;
s53, distributing residence time of sub residence points between the point A and the point B according to the calculated residence time node;
s54, carrying out convolution operation on the sub-resident points between the point A and the point B to obtain a continuous tool function between the point A and the point B；
S55, repeating the steps S51-S54, and calculating a continuous tool function set between all adjacent resident points after discretization of the processing track。
Preferably, the specific calculation process of step S52 is as follows:
searching the residence time t of the point A according to the residence time distribution of the cutter 1 And residence time t of point B 2 The residence time of the point A isThe residence time of point B is +.> The theoretical travel time on segment AB is then approximately +.>；
In the moving process from the point A to the point B, the moving process is divided into two sections, one section is an acceleration section, and the running time isThe method comprises the steps of carrying out a first treatment on the surface of the The other section is a constant speed section, and the running time is +.>；
Case (1): when the acceleration of the tool at the machine tool or robot execution end reaches a preset acceleration value, the theoretical residence time is satisfiedAnd a feed amount s;
；
wherein ,indicating acceleration of the tool, ++>Indicating the running speed of the cutter when the point A is reached;
and (3) finishing to obtain a vector equation:
；
will be、/> and />Is removed from the vector direction, is converted into a scalar equation,giving positive and negative numerical significance, wherein >0 is the positive direction of the coordinate system, and <0 is the negative direction of the coordinate system;
；
the solution of the time node scalar equation under which acceleration satisfies the operating condition is:
thus, the first and second heat exchangers are arranged,is the acceleration segment run time, i.e., residence time node;
case (2): when the acceleration of the tool at the machine tool or robot execution end does not reach the preset acceleration value, the actual running timeThe following scalar equation is satisfied:
the solution of the time node scalar equation under which acceleration does not meet the operating conditions is:
；
thus, the first and second heat exchangers are arranged,is a residence time node;
definition time-of-flight variable: actual residence time->Subtracting the theoretical residence time +.>Representing the time gain generated during the operation of points a and B as:
；
judging the running state of the machine tool or robot executing end, and solving the residence time node when the running state of the machine tool or robot executing end meets the condition (1) or (2) and />The case of (2) is as follows:
；
。
preferably, the specific calculation procedure of step S53 is as follows:
s531, for each sub-resident point inserted between the A point and the B pointSolving the resident time scalar equation to arrive at the moment +.>，/>：
When the condition (1) is satisfied:
when the condition (2) is satisfied:
wherein ,is the amount of sub-feed,/->Is an iferson bracket, whichThe definition is as follows:
；
p is an event that, when true,has a value of 1; when the event is false, < >>The value of (2) is 0;
after the completion of the solution of the displacement equation,the sequence represents a set of moments that reach each sub-dwell point when moving from point a to point B;
s532, pair ofFind the difference +.>The residence time of each sub-residence point is then made to be:
；
residence time allocation for successive tool function sub-residence points between points a and B,jrecorded by point A->。
Preferably, the step S54 specifically includes the following steps:
s541, expanding the tool influence function according to the variable expansion interval EDG;
s542, translating the tool influence function by a translation distance ofThen, performing the dimension expansion of the step S541; obtaining a dimension expansion matrix between the point A and the point B>；
S543, combining all the dimension expansion matrixesThe change removal rate of the feed speed influence of (a) is added to form a convolution operation to obtain a continuous tool function between the A point and the B point>：
；
wherein ,for a varying removal rate of the feed speed influence, < >>Representing the residence time coefficient at each sub-residence point,/for>Represents the removal rate at each sub-resident point, < ->An abscissa matrix representing a tool influence function, +.>Ordinate matrix representing tool influence function, +.>Matrix of removal rates representing tool influence functions, +.>An abscissa matrix representing a continuous tool influence function, < ->An ordinate matrix representing a continuous tool influence function,griddatabuilt-in for matlabgriddataFunction (F)>Is the interpolation mode of matlab.
Preferably, in step S541, the selection criterion of the dimension expansion range is that the continuous tool function dimension expansion area of points a and B includes the tool influence function dimension after feeding between points a and B, and the matrix after dimension expansion is recorded as，/>，/>。
Preferably, in step S6, the selection criterion of the dimension expansion range is that the full-caliber tool mark prediction area of the element is to include a removal size after the machining track is fed, and the removal size is greater than or equal to the size of the surface shape E of the workpiece to be machined; the matrix after recording and expanding is called as，/>，/>The surface shape with the tool mark is marked +.>：
；
。
Preferably, the specific procedure of step S1 is as follows:
s11, measuring the surface shape of the workpiece to be processed by using an interferometer, and comparing the surface shape with a target surface shape to obtain the removal amount distribution of the workpiece to be processedObtain->Discrete points->。
Preferably, the step S2 specifically includes the following steps:
s21, selecting an experimental piece which is made of the same material as a workpiece to be processed, and measuring the initial surface shape of the experimental piece;
s22, carrying out fixed-point timing polishing on the test piece, and measuring the surface shape of the polished test piece to obtain a polished surface shape;
and S23, subtracting the initial surface shape from the polishing surface shape, and dividing the polishing surface shape by the polishing time to obtain a tool influence function.
Preferably, the step S3 specifically includes the following steps:
setting a processing track type and a processing track parameter according to the size of a workpiece to be processed to obtainDiscrete polishing track points on the polishing track +.>The coordinates of the individual track points are denoted +.>In->The residence time of each track point is, wherein ,/>。
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a calculation method of a continuous tool function without aliasing under continuous motion mode control, which locally refines convolution characteristic information, and refines global tool removal characteristics by implementing a continuous tool function method on a full caliber of a surface shape, so that tool marks generated by tool feeding are reflected, and the prediction capability of an optical processing surface shape is improved.
Drawings
FIG. 1 is a flow chart of a method for predicting surface shape tool mark error based on continuous tool function according to an embodiment of the invention;
FIG. 2 is a schematic diagram of dimension expansion errors caused by translating ab-fragments, provided in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a situation where the length of a ab fraction is equal to an integer multiple of EDG, provided in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of a situation where the length of a ab fraction is not equal to an integer multiple of EDG, provided in accordance with an embodiment of the present invention;
FIG. 5 is a schematic diagram of the velocity change for the case when the acceleration provided according to an embodiment of the present invention is sufficient;
FIG. 6 is a schematic displacement diagram for different speed and acceleration conditions when the feed amount s >0 according to an embodiment of the present invention;
FIG. 7 is a schematic illustration of displacement for different speed, acceleration situations when the feed s <0, provided in accordance with an embodiment of the present invention;
FIG. 8 is a schematic diagram of a tool influence function for a single normalized removal rate provided in accordance with an embodiment of the present invention;
FIG. 9 is a schematic diagram of an expanded tool impact function provided according to an embodiment of the present invention;
FIG. 10 is a schematic diagram of a continuous tool function with no crosstalk or the like between points A and B after all the dimensions are expanded according to an embodiment of the present invention;
FIG. 11 is a schematic diagram of a cross-talk free non-isochronous continuous tool function between points A and B after full dimension expansion according to an embodiment of the present invention;
FIG. 12 is a schematic view of an initial surface shape of a workpiece to be processed according to an embodiment of the invention;
FIG. 13 is a schematic diagram of a tool influence function provided in accordance with an embodiment of the invention;
FIG. 14 is a schematic diagram of a grating trace provided in accordance with an embodiment of the present invention;
FIG. 15 is a schematic view of a surface shape of a workpiece to be processed (based on a grating processing trajectory) predicted according to a conventional prediction method;
FIG. 16 is a schematic view of the surface shape of a workpiece to be processed (based on a grating processing track) predicted by a prediction method according to an embodiment of the present invention;
FIG. 17 is a schematic diagram of a spiral machining trace provided in accordance with an embodiment of the present invention;
FIG. 18 is a schematic diagram of a surface shape after machining (based on a spiral machining track) of a workpiece to be machined predicted according to a conventional prediction method;
fig. 19 is a schematic diagram of a surface shape of a workpiece to be processed (based on a spiral processing track) predicted by a prediction method according to an embodiment of the present invention.
Detailed Description
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, like modules are denoted by like reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, a detailed description thereof will not be repeated.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not to be construed as limiting the invention.
As shown in fig. 1 to 19, the method for predicting the surface shape tool mark error based on the continuous tool function provided by the embodiment of the invention comprises the following steps:
s1, measuring the surface shape of a workpiece to be processed through an interferometer, and obtaining the discretized removal quantity distribution of the workpiece to be processed.
The specific process of step S1 is as follows:
s11, measuring the surface shape of the workpiece to be processed by using an interferometer, and comparing the surface shape with a target surface shape to obtain the removal amount distribution of the workpiece to be processedObtain->Discrete points->。
S2, selecting a machining mode of a workpiece to be machined, and measuring a tool influence function.
The invention is illustrated by taking a magneto-rheological tool influence function as an example, and the step S2 specifically comprises the following steps:
and S21, selecting an experimental piece which is made of the same material as the workpiece to be processed, and measuring the initial surface shape of the experimental piece.
And S22, carrying out fixed-point timing polishing on the test piece, and measuring the surface shape of the polished test piece to obtain a polished surface shape.
And S23, subtracting the initial surface shape from the polishing surface shape, and dividing the polishing surface shape by the polishing time to obtain a tool influence function.
S3, designing a machining track according to the size of the workpiece to be machined.
Setting polishing track type and polishing track parameters according to the size of the workpiece to be processed to obtainDiscrete polishing track points on the polishing trackiThe coordinates of the individual track points are denoted +.>In the followingFirst, theiThe residence time of each track point is, wherein ,/>。
And S4, calculating residence time distribution of the tool according to the machining track, the removal amount distribution and the tool influence function.
Order the；
(1.1)
wherein ,surface data point representing discretization->The removal of the part is marked as +.>。/>Stay point representing track discretization +.>The residence time at the site, designated +.>。/>The removal rate generated according to the discrete convolution relation of the surface shape data point and the resident point is marked as +.>。
The equation (1.1) is briefly described asThe system is called a residence time matrix equation, wherein R is a removal rate matrix generated by a surface-shaped data point grid and a residence point grid, M is the number of removed points, and N is the number of residence points;
(1.2)
(1.3)
(1.4)
(1.5)
(1.6)
(1.7)
in the formula ,is an objective function->Is the kth estimate of the objective function, +.>Is to gradient the function, < >>Is to calculate the i-th partial derivative of the function, < ->For the dwell time vector, +.>Is the residence time vector obtained by the kth iteration, E is the surface shape removal vector, ++>For the kth damping coefficient, the invention sets the initial damping coefficientβ0.1 @, @>For the kth iteration step, the invention sets the initial stepγ0.1 @, @>Is to project to the positive real set,/->Is the i-th component of the vector, +.>For the lower constraint of the dwell time solution, the present invention sets 0.1s,/for>For 2 norms of matrix or vector, delta is an iteration convergence condition, delta is set to be 0.01, B is a condition set, and specific details are provided in paper [ solving algorithm of magnetorheological processing residence time of large-caliber optical element ]]。
S5, calculating a continuous tool function between any two adjacent points on the processing track based on the residence time of the cutter.
The processing track in the invention is limited to the following two conditions, and any one of the two conditions can be satisfied, 1) the curvature of the track corner is large enough, and the standard of the large enough is: can lead the cutter to not generate rapid turning when continuously moving, and 2) the track corner or the rapid turning area is outside the net caliber.
The step S5 specifically comprises the following steps:
s51, discretizing a processing track into a limited resident point, arbitrarily selecting two adjacent resident points, marking the two adjacent resident points as a point A and a point B, and inserting sub-resident points between the point A and the point B for a tool influence function to carry out convolution operation; the relationship between the number of inserted sub-dwell points and the sampling interval of the tool-impact function is as follows:
(1.8)
wherein ,representing the number of inserted sub-dwell points, s representing the feed amount, EDG representing the variable dimension expansion interval, +.>Represents any integer, +.>Representing a positive integer set.
Taking such integer points, there is no aliasing in the computed continuous tool function. The reasons are as follows:
for convenience of discussion of aliasing, a variable dimension-expanding interval (expand dimension gap, EDG) is defined, two adjacent points are arbitrarily selected on the track, the starting point is A, the end point is B, and the length of the AB section is a feed amount s. According toThe number of points divides the AB segment (comprising the end points A and B), wherein the single segment divided into is called AB, the divided nodes (such as a and B) are called continuous tool function sub-resident points, and the length is +.>. Thus, the error caused by the translation distance ab is shown in fig. 2.
As shown in fig. 3, if the length of the ab segment is equal to an integer multiple of the EDG:
(1.9)
as shown in fig. 4, if the length of the ab segment is not equal to an integer multiple of the EDG:
(1.10)
wherein e, n, m, k, f represents only a certain integer, the meaning of (1.9) and (1.10) is that a positive integer is always found by this iterationSo that the period is +.>Is just +.>Is free of aliasing display.
ab determines the sampling interval, while EDG is the recording interval of the signal, according to the Nyquist sampling theorem,on the other hand, ab needs to be divided by s to obtain the expression (1.8), and h is an integer because of the convenience of calculation.
S52, calculating residence time nodes for distributing sub-residence points between the point A and the point B.
On the trajectory, a family of continuous tool functions is computed between every two adjacent dwell points. The step is detailed by calculating a continuous tool function between two points of the grating track.
Searching the residence time t of the point A according to the residence time distribution of the cutter calculated in the step S4 1 Point B residence time t 2 The residence time of the point A isThe residence time of point B is +.>The theoretical travel time on segment AB is then approximately +.>。
In the moving process from the point A to the point B, the moving process is divided into two sections, one section is called an acceleration section, and the running time is thatThe other section is called constant speed section, the running time is +.>As shown in fig. 5.
Case (1): when the acceleration of the tool at the machine tool or robot execution end reaches a preset acceleration value, the theoretical residence time is satisfiedAnd a feed amount s;
；
wherein ,indicating acceleration of the tool, ++>Indicating the running speed of the cutter when the point A is reached;
and (3) finishing to obtain a vector equation:
；
will be、/> and />The vector direction of (2) is removed and is converted into a scalar equation, positive and negative numerical significance is given, wherein >0 is the positive direction of the coordinate system, and <0 is the negative direction of the coordinate system;
；
the solution of the time node scalar equation under which acceleration satisfies the operating condition is:
thus, the first and second heat exchangers are arranged,is the acceleration segment run time, i.e., residence time node;
case (2): when the acceleration of the tool at the machine tool or robot execution end does not reach the preset acceleration value, the actual running timeThe following scalar equation is satisfied:
the solution of the time node scalar equation under which acceleration does not meet the operating conditions is:
；
thus, the first and second heat exchangers are arranged,is a residence time node;
definition time-of-flight variable: actual residence time->Subtracting the theoretical residence time +.>Representing that the time gain generated in the operation process of the point A and the point B is as follows:
judging the running state of the machine tool or robot execution end, carrying out classified discussion on the meeting conditions (1) and (2), and solving the residence time node and />Is the case: />
When the execution end moves from the point A to the point B in the positive direction of the coordinate system and moves in the positive direction of the coordinate system from the point A, the following steps are:
rate when at point aWhen the feeding amount s is equal to the theoretical speed determined by the theoretical travel time t, the running displacement condition is as shown in (3) of fig. 6, namely:
；
rate when at point aAbove the theoretical rate determined by the feed s and the theoretical travel time t, a deceleration, i.e. +.>The method comprises the steps of carrying out a first treatment on the surface of the When the speed is not more than +.>When the condition (1) is satisfied, the running displacement condition is as shown in (2) of FIG. 6, i.eThe method comprises the steps of carrying out a first treatment on the surface of the When (when)Speed exceeds->When the condition (2) is satisfied, the running displacement condition is as shown in (1) of FIG. 6, i.e. +.>The method is characterized by comprising the following steps:
rate when at point aIf the speed is smaller than the theoretical speed determined by the feed amount s and the theoretical travel time t, the acceleration should be performed so as not to break the constraint of the feed amount s, namely +.>The method comprises the steps of carrying out a first treatment on the surface of the When the speed is not lower than +.>When the condition (1) is satisfied, the running speed condition is as shown in (4) of FIG. 6, i.e. +.>. When the speed is lower than +.>When the condition (2) is satisfied, the running speed condition is as shown in (6) of FIG. 6, i.e. +.>The method is characterized by comprising the following steps:
when the execution end moves from the point A to the point B in the negative direction of the coordinate system and moves from the point A to the point B in the negative direction of the coordinate system, the following steps are:
rate when at point aWhen the feeding amount s is equal to the theoretical speed determined by the theoretical travel time t, the running displacement condition is as shown in (3) of fig. 7, namely: />
Rate when at point aGreater than the theoretical rate determined by the feed rate s and the theoretical travel time t [ absolute value is small ]]Acceleration should be performed so as not to break the constraint of the feed amount s, i.e. +.>The method comprises the steps of carrying out a first treatment on the surface of the When the speed is not more than +.>When the condition (1) is satisfied, the running speed condition is shown as (4) in FIG. 7, namely +.>The method comprises the steps of carrying out a first treatment on the surface of the When the speed exceeds +.>When the condition (2) is satisfied, the running speed condition is shown as (6) in FIG. 7, namely +.>The method is characterized by comprising the following steps:
rate when at point aLess than the theoretical rate determined by the feed rate s and the theoretical travel time t[ absolute value is large]The deceleration should be performed so as not to break the constraint of the feed amount s, i.e. +.>The method comprises the steps of carrying out a first treatment on the surface of the When the speed is not lower than +.>When (1) is satisfied, the running speed is shown as (2) in FIG. 7, namely +.>The method comprises the steps of carrying out a first treatment on the surface of the When the speed is lower than +.>When (2) is satisfied, the running speed is shown as (1) in FIG. 7, namely +.>The method is characterized by comprising the following steps:
when the execution end moves from the point A to the point B in the positive direction of the coordinate system, but moves in the negative direction of the coordinate system before reaching the point A, the sharp turn occurs, namely:
rate when at point aIs greater than->When the condition (1) is satisfied, the running speed condition is shown as (5) in FIG. 6, namely +.>The method comprises the steps of carrying out a first treatment on the surface of the When the speed is lower than +.>When full ofFoot condition (2), running speed condition as shown in (7) of FIG. 6, isThe method is characterized by comprising the following steps: />
When the execution end moves from point a to point B in the negative direction of the coordinate system, but moves in the positive direction of the coordinate system before reaching point a, a sharp turn occurs:
rate when at point aLess than->When the condition (1) is satisfied, the running speed condition is shown as (5) in FIG. 7, namely +.>The method comprises the steps of carrying out a first treatment on the surface of the When the speed is lower than +.>When the condition (2) is satisfied, the running speed condition is as shown in (7) of FIG. 7, namelyThe method is characterized by comprising the following steps:
the special description is made for the above [3] and [4], and in the actual process, the machine tool magneto-rheological technology or the robot magneto-rheological technology is considered, because two assumptions of continuous direction change of the track or the situation happens outside the net caliber, the surface shape removal amount of the net caliber is not influenced; or this does not occur, the considerations of [3] and [4] do not require additional restrictions on the two magnetorheological technology carriers, and do not affect the determination of the residence time distribution node.
And S53, distributing residence time of each sub-residence point between the point A and the point B according to the calculated time node.
The specific calculation process of step S53 is as follows:
s531, dividing each sub-resident point after ABSolving the resident time scalar equation to arrive at the moment +.>，/>：
Satisfy case (1):
；
satisfy case (2):
wherein ,is an iferson bracket, which is defined as follows:
；
p is an event that, when true,has a value of 1; when the event is false, < >>Has a value of 0, e.g.>；
After the completion of the solution of the displacement equation,the sequence represents the set of moments that reach each sub-dwell point when moving from point a to point B.
S532, pair ofFind the difference +.>The residence time of each sub-residence point is then made to be:
；
residence time allocation for successive tool function sub-residence points between points a and B,jrecorded by point A->。
S54, carrying out convolution operation on the distribution point between the point A and the point B.
Taking the magnetorheological tool influence function as an example, fig. 8 shows the magnetorheological tool influence function of normalized removal rate under a certain process.
The step S54 specifically includes the following steps:
s541, expanding the tool influence function according to the dimension expansion interval.
In step S541, the selection criteria of the expanded dimension range is that the area includes the tool-affected function size after the AB-segment feed, and the matrix after the expansion is recorded as，/>，/>. The dimension expansion method may use a function of matlab,and also multiply by a coefficient +>I.e. the rate of removal of the change of the influence of the feed speed +.>As shown in fig. 9.
S542, translating the tool influence function by a translation distance ofPerforming step 541 dimension expansion; obtaining a dimension expansion matrix between AB segments>。
S543, combining all the dimension expansion matrixesThe change removal rate of the feed speed influence is added to obtain a continuous tool function between AB points:
；
；
wherein ,for a varying removal rate of the feed speed influence, < >>Representing the residence time coefficient at each sub-residence point,/for>Represents the removal rate at each sub-resident point, < ->An abscissa matrix representing a tool influence function, +.>Ordinate matrix representing tool influence function, +.>Matrix of removal rates representing tool influence functions, +.>An abscissa matrix representing a continuous tool influence function, < ->An ordinate matrix representing a continuous tool influence function.
In order to ensure the smoothness and naturality of interpolation, a built-in griddata function of matlab is selected, and an interpolation mode selects an 'natural' mode.
Displaying its available matlab commandsAs shown in fig. 10 and 11. />
S55, repeating the steps S51-S54, and calculating a continuous tool function set between all adjacent residence points after discretization of the processing track。
S6, expanding all the continuous tool functions, and predicting the surface shape tool mark error of the workpiece to be processed.
In step S6, the selection criterion of the dimension expansion range is that the region includes a removal dimension after the machining track is fed, and the removal dimension is greater than or equal to the dimension of the surface shape E of the workpiece to be machined; the matrix after recording and expanding is called as，/>，The dimension expansion method can use matlab function,/for the dimension expansion method>The surface shape with the tool mark is marked +.>The +.can be given by this formula>Display its available matlab command +.>Thus, the prediction of the surface shape tool mark of the continuous tool function is completed.
Conventional surface shape prediction is a method relying on numerical convergence, and the coarsening convolution process, due to the limitation of mathematical definition of discrete convolution, is to make the interval between discrete dwell points equal to the interval between functions to be removed, which usually causes the functions to be lost by a downsampling tool, and the numerical values are globally converged, not locally converged.
The continuous tool function is a numerical convergence process involving all sampling points of the tool influence function, and is a method for refining local information. By implementing continuous tool function calculation on adjacent resident points of full-caliber track discretization, the details of removal among each adjacent point are shown, so that the tool mark is reflected.
And (3) complete demonstration: the initial surface shape of the workpiece to be processed, the tool influence function and the track are obtained as grating tracks, as shown in fig. 12, 13 and 14, respectively, the surface shape of the workpiece to be processed predicted by the traditional prediction method is shown in fig. 15, wherein the surface shape only shows prediction on low-frequency errors, and no tool mark error is shown. The surface shape of the workpiece to be processed predicted by the prediction method provided by the invention is shown in fig. 16, wherein the surface shape is predicted by low-frequency error prediction and the tool mark generated by feeding the tool grating track. The same initial surface shape and tool influence function are adopted, but the track is selected as a spiral track (shown in fig. 17), the surface shape of the workpiece to be processed predicted by the traditional prediction method is shown in fig. 18, wherein the surface shape only shows prediction on low-frequency errors, and no tool mark error is shown. The surface shape of the workpiece to be processed predicted by the prediction method provided by the invention is shown in fig. 19, wherein the surface shape is predicted by low-frequency error prediction and the tool mark generated by feeding the spiral track of the tool.
The invention provides a surface shape tool mark error prediction method based on a continuous tool function, and aims to improve the local detail prediction capability. Compared with the limitation that the traditional surface shape prediction method only depends on two norms can only predict the surface shape low-frequency error morphology at the position, the novel method further digs the fine information of local processing on the basis of the traditional method, so that tool feeding trace (namely tool mark) is predicted, surface shape prediction means are enriched, and the surface shape prediction capability is remarkably improved.
It should be appreciated that various forms of the flows shown above may be used to reorder, add, or delete steps. For example, the steps described in the present disclosure may be performed in parallel, sequentially, or in a different order, provided that the desired results of the technical solutions of the present disclosure are achieved, and are not limited herein.
The above embodiments do not limit the scope of the present invention. It will be apparent to those skilled in the art that various modifications, combinations, sub-combinations and alternatives are possible, depending on design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of the present invention.

Claims (10)

1. A surface shape tool mark error prediction method based on continuous tool functions comprises the following steps:
s1, measuring the surface shape of a workpiece to be processed through an interferometer, and obtaining discretized removal quantity distribution of the workpiece to be processed;
s2, selecting a processing mode of the workpiece to be processed, and measuring a tool influence function;
s3, designing a machining track according to the size of the workpiece to be machined;
the method is characterized by further comprising the following steps:
s4, calculating residence time distribution of the tool according to the machining track, the removal amount distribution and the tool influence function;
s5, calculating a continuous tool function between any two adjacent points on the processing track based on residence time distribution of the cutter;
s6, carrying out dimension expansion on all continuous tool functions to the full caliber size of the workpiece to be processed, adding, and predicting the surface shape tool mark error of the workpiece to be processed.
2. The method for predicting surface shape tool mark error based on continuous tool function as claimed in claim 1, wherein the step S5 specifically comprises the steps of:
s51, discretizing the processing track into a limited resident point, arbitrarily selecting two adjacent resident points, namely an A point and a B point, and inserting sub-resident points between the A point and the B point to enable the tool influence function to carry out convolution operation; the relationship between the number of inserted sub-dwell points and the sampling interval of the tool-impact function is as follows:
；
wherein ,representing the number of inserted sub-dwell points, s representing the feed amount, EDG representing the variable dimension expansion interval, +.>Representing any one ofAn integer, & gt>Representing a positive integer set;
s52, calculating residence time nodes for distributing sub-residence points between the point A and the point B;
s53, distributing residence time of sub residence points between the point A and the point B according to the calculated residence time node;
s54, carrying out convolution operation on the sub-resident points between the point A and the point B to obtain a continuous tool function between the point A and the point B；
S55, repeating the steps S51-S54, and calculating a continuous tool function set between all adjacent residence points after discretization of the processing track。
3. The method for predicting surface shape tool mark error based on continuous tool function as claimed in claim 2, wherein the specific calculation process of step S52 is as follows:
searching the residence time t of the point A according to the residence time distribution of the cutter 1 And residence time t of point B 2 The residence time of the point A isThe residence time of point B is +.>The theoretical travel time on segment AB is approximately；
In the moving process from the point A to the point B, the moving process is divided into two sections, one section is an acceleration section, and the running time isThe method comprises the steps of carrying out a first treatment on the surface of the The other section is a constant speed section, and the running time is +.>；
Case (1): when the acceleration of the tool at the machine tool or robot execution end reaches a preset acceleration value, the theoretical residence time is satisfiedAnd a feed amount s;
；
wherein ,indicating acceleration of the tool, ++>Indicating the running speed of the cutter when the point A is reached;
and (3) finishing to obtain a vector equation:
；
will be、/> and />The vector direction of (2) is removed and is converted into a scalar equation, positive and negative numerical significance is given, wherein >0 is the positive direction of the coordinate system, and <0 is the negative direction of the coordinate system;
；
the solution of the time node scalar equation under which acceleration satisfies the operating condition is:
；
thus, the first and second heat exchangers are arranged,is the acceleration segment run time, i.e., residence time node;
case (2): when the acceleration of the tool at the machine tool or robot execution end does not reach the preset acceleration value, the actual running timeThe following scalar equation is satisfied:
the solution of the time node scalar equation under which acceleration does not meet the operating conditions is:
；
thus, the first and second heat exchangers are arranged,is a residence time node;
definition time-of-flight variable: actual residence time->Subtracting the theoretical residence time +.>Representing the time gain generated during the operation of points a and B as:
；
judging the running state of the machine tool or robot executing end, and solving the residence time node when the running state of the machine tool or robot executing end meets the condition (1) or (2) and />The case of (2) is as follows:
；
。
4. the method for predicting surface shape tool mark error based on continuous tool function as set forth in claim 3, wherein the specific calculation process of step S53 is as follows:
s531, for each sub-resident point inserted between the A point and the B pointSolving the resident time scalar equation to arrive at the moment +.>，/>：
When the condition (1) is satisfied:
when the condition (2) is satisfied:
wherein ,is the amount of sub-feed,/->Is an iferson bracket, which is defined as follows:
；
p is an event that, when true,has a value of 1; when the event is false, < >>The value of (2) is 0;
after the completion of the solution of the displacement equation,the sequence represents a set of moments that reach each sub-dwell point when moving from point a to point B;
s532, pair ofFind the difference +.>The residence time of each sub-residence point is then made to be:
；
residence time allocation for successive tool function sub-residence points between points a and B,jrecorded by point A->。
5. The method for predicting surface form tool mark error based on continuous tool function as claimed in claim 4, wherein the step S54 specifically comprises the steps of:
s541, expanding the tool influence function according to the variable expansion interval EDG;
s542, translating the tool influence function by a translation distance ofThen, performing the dimension expansion of the step S541; obtaining a dimension expansion matrix between the point A and the point B>；
S543, combining all the dimension expansion matrixesThe change removal rate of the feed speed influence of (a) is added to form a convolution operation to obtain a continuous tool function between the point A and the point B>：
；
wherein ,for a varying removal rate of the feed speed influence, < >>Representing the residence time coefficient at each sub-residence point,/for>Represents the removal rate at each sub-resident point, < ->An abscissa matrix representing a tool influence function, +.>Ordinate matrix representing tool influence function, +.>Matrix of removal rates representing tool influence functions, +.>An abscissa matrix representing a continuous tool influence function, < ->An ordinate matrix representing a continuous tool influence function,griddatabuilt-in for matlabgriddataFunction (F)>Is the interpolation mode of matlab.
6. The method according to claim 5, wherein in step S541, the selection criterion of the dimension expansion range is that the dimension expansion area of the continuous tool function of points a and B includes the tool influence function size after feeding between points a and B, and the matrix after dimension expansion is recorded as，/>，/>。
7. The method according to claim 5, wherein in step S6, the selection criterion of the dimension expansion range is that the full-caliber tool mark prediction area of the element is to include a removal size after the feeding of the machining track, and the removal size is greater than or equal to the size of the surface shape E of the workpiece to be machined; the matrix after recording and expanding is called as，/>，/>The surface shape with the tool mark is marked +.>：
；
。
8. The method for predicting surface shape tool mark error based on continuous tool function as claimed in claim 1, wherein the specific process of step S1 is as follows:
measuring the surface shape of the workpiece to be processed by using an interferometer and forming the surface shape with the target surfaceObtaining the removal amount distribution of the workpiece to be processed by row comparisonObtain->Discrete points->，MIndicating the number of removed points.
9. The method for predicting surface shape tool mark error based on continuous tool function as claimed in claim 1, wherein the step S2 specifically comprises the steps of:
s21, selecting an experimental piece which is made of the same material as the workpiece to be processed, and measuring the initial surface shape of the experimental piece;
s22, carrying out fixed-point timing polishing on the test piece, and measuring the surface shape of the polished test piece to obtain a polished surface shape;
and S23, subtracting the initial surface shape from the polishing surface shape, and dividing the polishing surface shape by the polishing time to obtain the tool influence function.
10. The method for predicting surface shape tool mark error based on continuous tool function as claimed in claim 1, wherein the step S3 specifically comprises the steps of:
setting a processing track type and a processing track parameter according to the size of the workpiece to be processed to obtainDiscrete polishing track points on the polishing track +.>The coordinates of the individual track points are denoted +.>In->The residence time of each track point is, wherein ,/>，NRepresenting the number of dwell points.
CN202310967454.5A 2023-08-03 2023-08-03 Surface shape tool mark error prediction method based on continuous tool function Active CN116679622B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310967454.5A CN116679622B (en) 2023-08-03 2023-08-03 Surface shape tool mark error prediction method based on continuous tool function

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310967454.5A CN116679622B (en) 2023-08-03 2023-08-03 Surface shape tool mark error prediction method based on continuous tool function

Publications (2)

Publication Number Publication Date
CN116679622A true CN116679622A (en) 2023-09-01
CN116679622B CN116679622B (en) 2023-10-03

Family

ID=87785889

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310967454.5A Active CN116679622B (en) 2023-08-03 2023-08-03 Surface shape tool mark error prediction method based on continuous tool function

Country Status (1)

Country Link
CN (1) CN116679622B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117473802A (en) * 2023-12-28 2024-01-30 中国科学院长春光学精密机械与物理研究所 Method for rapidly solving polishing residence time of large-caliber optical element

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5291415A (en) * 1991-12-13 1994-03-01 Hughes Aircraft Company Method to determine tool paths for thinning and correcting errors in thickness profiles of films
CN102501180A (en) * 2011-10-26 2012-06-20 中国科学院光电技术研究所 Method for correcting errors of imprinting effect of light reflector
CN105328535A (en) * 2015-09-29 2016-02-17 中国人民解放军国防科学技术大学 Nanometer-precision optical curved-face ion beam processing method based on non-linear modeling
CN106181741A (en) * 2016-07-13 2016-12-07 中国工程物理研究院机械制造工艺研究所 Based on becoming the Jet Polishing face shape error control method removing function
CN107520683A (en) * 2017-08-31 2017-12-29 中国工程物理研究院激光聚变研究中心 The contour paths planning method of rim of the mouth footpath polishing
CN113275976A (en) * 2020-02-20 2021-08-20 中国科学院长春光学精密机械与物理研究所 Computer-controlled optical surface shape error convergence processing method, device and medium
CN115952568A (en) * 2022-12-16 2023-04-11 上海交通大学 Smooth polishing path planning method and system with regional adaptability

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5291415A (en) * 1991-12-13 1994-03-01 Hughes Aircraft Company Method to determine tool paths for thinning and correcting errors in thickness profiles of films
CN102501180A (en) * 2011-10-26 2012-06-20 中国科学院光电技术研究所 Method for correcting errors of imprinting effect of light reflector
CN105328535A (en) * 2015-09-29 2016-02-17 中国人民解放军国防科学技术大学 Nanometer-precision optical curved-face ion beam processing method based on non-linear modeling
CN106181741A (en) * 2016-07-13 2016-12-07 中国工程物理研究院机械制造工艺研究所 Based on becoming the Jet Polishing face shape error control method removing function
CN107520683A (en) * 2017-08-31 2017-12-29 中国工程物理研究院激光聚变研究中心 The contour paths planning method of rim of the mouth footpath polishing
CN113275976A (en) * 2020-02-20 2021-08-20 中国科学院长春光学精密机械与物理研究所 Computer-controlled optical surface shape error convergence processing method, device and medium
CN115952568A (en) * 2022-12-16 2023-04-11 上海交通大学 Smooth polishing path planning method and system with regional adaptability

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
李龙响;郑立功;邓伟杰;王孝坤;李丽富;白杨;张学军;: "应用四轴联动磁流变机床加工曲面", 光学精密工程, no. 10, pages 2820 - 2826 *
黄登鹏: "离轴三反光学自由曲面抛光工艺研究", 《中国优秀硕士学位论文全文库 工程科技Ⅱ辑》, no. 09, pages 1 - 56 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117473802A (en) * 2023-12-28 2024-01-30 中国科学院长春光学精密机械与物理研究所 Method for rapidly solving polishing residence time of large-caliber optical element
CN117473802B (en) * 2023-12-28 2024-03-19 中国科学院长春光学精密机械与物理研究所 Method for rapidly solving polishing residence time of large-caliber optical element

Also Published As

Publication number Publication date
CN116679622B (en) 2023-10-03

Similar Documents

Publication Publication Date Title
CN116679622B (en) Surface shape tool mark error prediction method based on continuous tool function
JP5280863B2 (en) Piecewise meshing and neighborhood search for object interaction simulation
Dee Simplification of the Kalman filter for meteorological data assimilation
CN103345577B (en) Variation Bayesian probability assumed density multi-object tracking method
CN110412877B (en) Optimal control method for shipboard aircraft deck path planning based on NSP algorithm
Li et al. Thermal positioning error modeling of machine tools using a bat algorithm-based back propagation neural network
Hodonou et al. Material-design-process selection methodology for aircraft structural components: application to additive vs subtractive manufacturing processes
CN104007705A (en) Prospective interpolation system for compressing and smoothening small segment paths
CN109977098A (en) Non-stationary time-series data predication method, system, storage medium and computer equipment
Aich et al. Application of teaching learning based optimization procedure for the development of SVM learned EDM process and its pseudo Pareto optimization
CN107169616B (en) Relative entropy prediction method for relative complexity of mine non-mining area structure
CN108319799A (en) A kind of more fidelity optimum design methods of the shape of Autonomous Underwater Vehicle
CN104898562A (en) Modeling method of thermal error compensation of numerically-controlled machine tool
CN110766060B (en) Time series similarity calculation method, system and medium based on deep learning
CN110640736A (en) Mechanical arm motion planning method for intelligent manufacturing
CN114611340A (en) Coupling Euler-Lagrange method for accurately capturing shock wave propagation process
JP5113765B2 (en) Discretization of objects into particles for computer simulation and analysis
CN106485030B (en) A kind of symmetrical border processing method for SPH algorithm
Heitmann et al. Numerical determination of equivalent damping parameters for a finite element model to predict the underwater noise due to offshore pile driving
CN104331080B (en) For the fixed point track path planing method of mobile robot
Scholtes et al. Advances in level-set modeling of recrystallization at the polycrystal scale-development of the digi-μ software
CN106203526A (en) Target behavior pattern online classification method based on multidimensional characteristic
Lai et al. Probabilistic approach to mechanism reliability with multi-influencing factors
Sarakinos et al. Exploring freeform deformation capabilities in aerodynamic shape parameterization
Clarich et al. A Competitive Game Approach for Multi Objective Robust Design Optimization

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant