CN109765843B - Thin-wall part machining error compensation method based on mirror image method and cubic spline interpolation - Google Patents
Thin-wall part machining error compensation method based on mirror image method and cubic spline interpolation Download PDFInfo
- Publication number
- CN109765843B CN109765843B CN201910026178.6A CN201910026178A CN109765843B CN 109765843 B CN109765843 B CN 109765843B CN 201910026178 A CN201910026178 A CN 201910026178A CN 109765843 B CN109765843 B CN 109765843B
- Authority
- CN
- China
- Prior art keywords
- machining
- compensation
- interpolation
- cubic spline
- mirror image
- 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.)
- Active
Links
Images
Abstract
The invention discloses a thin-wall part machining error compensation method based on a mirror image method and cubic spline interpolation, which comprises the steps of sequentially machining an initial blank to a position with a certain allowance and obtaining a machining error e of a corresponding sampling point by using an on-machine detection systemkAnd the actual depth of cut value ykCalculating to obtain a compensation coefficient alphakFurther obtaining the nominal cutting depth x in the next compensation processingk+1Finally, generating a limited number of interpolation points according to the size of the interpolation interval by utilizing a cubic spline interpolation method so as to obtain an optimal tool machining path; the method is based on-machine detection data, an optimized mirror error compensation model is established by introducing a compensation coefficient, and a cubic spline interpolation method is combined to generate enough interpolation points to obtain an optimal cutter machining path, so that the machining error compensation model of the thin-wall part is simplified, the compensation efficiency is improved, and the machining precision is ensured.
Description
Technical Field
The invention relates to the technical field of machine tool precision cutting machining, in particular to a thin-wall part machining error compensation method based on a mirror image method and cubic spline interpolation.
Background
With the change of numerical control machining technology, the machining precision requirement on thin-wall parts in the fields of die manufacturing, optical instruments, aerospace, medical treatment and the like is higher and higher, and whether high-precision products can be produced or not becomes a standard for measuring the national manufacturing level. During the actual cutting process, the force thermal coupling effect generated by the relative motion between the tool and the workpiece causes the tool to generate continuous elastic-plastic deformation and severe vibration phenomena, so that a deviation value exists between the machined actual surface and the machined design surface of the workpiece, and the deviation value is finally expressed in the form of machining error. Too large processing errors can affect the quality of products and even cause resource waste. Therefore, it is important to compensate for the necessary machining error of the thin-walled member.
The existing thin-wall part processing error compensation method mainly comprises the following steps that firstly, error compensation is carried out by utilizing a part three-dimensional model, and the published patent application 201510192630.8 provides an online measuring and compensating processing method for the milling deformation of a thin-wall part, wherein the method comprises the steps of calculating the deviation value of the part by comparing the three-dimensional model of the part with the actual size of a corresponding measuring point, and applying a compensation coefficient to optimize a processing track on the basis of the deviation value, so that compensation processing is carried out; secondly, compensation processing is carried out by utilizing the idea of iteration, and the published patent application 201611251817.1 provides an aeroengine thin-wall blade processing error compensation method based on a learning algorithm, and the method adopts an algorithm combining Taylor expansion, Newton iteration and blade process flexibility to establish an error compensation model and carry out error compensation for the basis; thirdly, error compensation is carried out by utilizing a finite element method, and the published patent application 201710454083.5 provides a method for compensating the cutting error of the thin-wall part made of the hard and brittle material.
However, the above three methods have disadvantages in that: firstly, the compensation process is complex, particularly an iterative method and a finite element method, a complex mathematical formula or a mechanical model needs to be established, the compensation efficiency is low, and the application in actual production is not facilitated; secondly, the coupling effect of the compensation quantity on the processing deformation is neglected, so that the accumulated error generated in the compensation process cannot be compensated in time, and the compensation effect is influenced to a certain extent; thirdly, the compensation values of the discrete positions are not smoothed, and the surface of the compensated workpiece is easy to present a fine step shape, thereby influencing the processing precision. Therefore, it is necessary to develop a thin-wall part machining error compensation method capable of solving the above-mentioned defects.
Disclosure of Invention
The invention aims to overcome the defects of complex compensation process, low compensation efficiency, neglected influence of compensation quantity on machining deformation and the like in the conventional machining error compensation method, and provides a thin-wall part machining error compensation method based on a mirror image method and cubic spline interpolation.
Therefore, the technical scheme of the invention is as follows:
a thin-wall part machining error compensation method based on a mirror image method and cubic spline interpolation comprises the following steps:
s1, processing the initial blank until a certain margin is left;
s2, using the on-machine detection system to detect the machining error e of the workpiece surface according to a certain sampling point sequence on the workpiece surface after the step S1k＝{ek1、ek2、…、eknAnd calculating the actual cutting depth value y of the corresponding sampling point sequencek＝{yk1、yk2、…、ykn}；
S3, establishing an optimized error compensation model based on a mirror image method:
s301, substituting machining errors and actual cutting depth values of the n sampling points obtained in the step S2 into a compensation coefficient alphakThe calculation formula of (2):
obtaining the compensation coefficient alpha of n sampling points ═ ak1、ak2、…、akn}; wherein x iskIn order to perform step S1, n sampling points are used to obtain the nominal cutting depth, x, of the previous cutting processk＝{xk1、xk2、…、xkn}；
S302, substituting the compensation coefficient alpha into a mirror image method compensation formula:
xk+1＝xk+αk·ekthe compound of the formula (2),
carrying out error compensation optimization to obtain the nominal cutting depth x in the next compensation processingk+1(ii) a Wherein x isk+1＝{xk1+1、xk2+1、…、xkn+1}；
S4, the nominal cutting depth x of the n sampling points obtained in the step S3 in the next compensation machiningk+1As an interpolation node, generating a limited number of interpolation points according to the size of an interpolation interval by utilizing a cubic spline interpolation method so as to obtain an optimal tool machining path;
s5, finishing compensation machining according to the optimal cutter machining path obtained in the step S4, and detecting machining errors of the machining compensation surface by using an on-machine detection system:
1) if the maximum value of the machining error falls into the tolerance range, stopping compensation machining, and finishing machining of the workpiece;
2) and if the maximum value of the machining error exceeds the tolerance range, repeating the steps S2-S4 until the maximum value of the machining error falls within the tolerance range.
Further, in the step S1, the machining allowance of the initial blank is usually 2 to 3 mm.
Further, in the above step S2, the setting principle of the sampling points is: and setting a sampling point at every interval of 5-10 mm.
Further, the specific step in step S4 is:
s401, the n nominal cutting depths x obtained in the step S3k+1As a given interpolation node, where a ═ xk1+1<xk2+1<…<xkn+1＝b，[a,b]Is an interpolation interval;
s402, substituting the interpolation node into an interpolation function equation:
Si(x)＝ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3the compound of the formula (3),
wherein, in formula (3), ai、bi、ciAnd diIs constant, i ═ {0, 1, …, n }; the cubic spline interpolation function is a polynomial not more than cubic, the second order of which is conductive and continuous, and x of the boundary interpolation node of the interpolation intervalkn+1And xkn+1The first derivative values are equal and the second derivative value is 0.
And S403, establishing an equation set according to the boundary conditions of the interpolation function, and performing simultaneous solution to obtain cubic spline interpolation function values of the n interpolation nodes.
Further, in step S4, 1-3 difference points are generated between every two interpolation nodes.
Compared with the prior art, the thin-wall part machining error compensation method based on the mirror image method and the cubic spline interpolation optimizes the mirror image compensation method and combines the cubic spline interpolation method to compensate the machining error, the compensation process is simple, the compensation machining precision is effectively improved compared with the traditional mirror image compensation method, and the compensation times are reduced; in actual production, for the situation of batch production and processing, after a relatively stable process flow and specifications are formed, under the condition that cutting parameters are not changed, the processing error distribution can show a certain rule, the method can be used for calculating a nominal value of the cutting depth in the compensation processing of small-batch workpieces, and an optimal general compensation processing program is obtained after statistical analysis and is used for the production and processing of subsequent large-batch workpieces so as to improve the production efficiency.
Drawings
FIG. 1 is a schematic flow chart of the thin-wall part machining error compensation method based on the mirror image method and cubic spline interpolation.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, which are not intended to limit the invention in any way.
The following process of performing error compensation machining on a thin-wall aluminum alloy workpiece by adopting a thin-wall workpiece machining error compensation method for a mirror image method and cubic spline interpolation is described in detail as follows:
as shown in fig. 1, the thin-wall part machining error compensation method comprises the following steps:
s1, processing the initial blank until a certain margin is left for 3 mm;
s2, using the on-machine detection system to detect the machining error e of the workpiece surface according to a certain sampling point sequence on the workpiece surface after the step S1k＝{ek1、ek2、…、eknAnd calculating the actual cutting depth value y of the corresponding sampling point sequencek＝{yk1、yk2、…、ykn}; specifically, the sampling points are arranged one by one at intervals of 10mm along the length extension direction of the machined surface of the workpiece;
s3, establishing an optimized error compensation model based on a mirror image method:
s301, substituting the machining error and the actual cutting depth value of each sampling point obtained in the step S2 into the compensation coefficient alphakFormula (1):
obtaining the compensation coefficient alpha ═ a of each sampling pointk1、ak2、…、akn}; wherein x iskIn step S1, the nominal cutting depth x of each sample point in the previous cutting processk＝{xk1、xk2、…、xkn}；
S302, substituting the compensation coefficient alpha into a mirror image method compensation formula, wherein the optimized error compensation general calculation formula is (2): x is the number ofk+1＝xk+αk·ekObtaining the nominal cutting depth x in the next compensation processingk+1(ii) a Wherein x isk+1＝{xk1+1、xk2+1、…、xkn+1}；
S4, the nominal cutting depth x of each sampling point obtained in the step S3 in the next compensation machiningk+1As interpolation nodes, generating a limited number of interpolation points according to the size of an interpolation interval by utilizing a cubic spline interpolation method, namely generating 1-3 difference points between every two interpolation nodes to obtain an optimal tool machining path;
the specific steps of step S4 are:
s401, calculating each nominal cutting depth x obtained in step S3k+1As a given interpolation node, where a ═ xk1+1<xk2+1<…<xkn+1＝b，[a,b]Is an interpolation interval;
s402, substituting the interpolation node into an interpolation function equation:
Si(x)＝ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3the compound of the formula (3),
wherein, in formula (3), ai、bi、ciAnd diIs constant, i ═ {0, 1, …, n }; the third mentionedThe sub-spline interpolation function is a polynomial not more than three times, the cubic spline interpolation function is a second-order conduction and continuous, and x of the boundary interpolation node of the interpolation intervalkn+1And xkn+1The first derivative values are equal and the second derivative value is 0.
S403, establishing an equation set according to the boundary conditions of the interpolation function, and simultaneously solving to obtain a cubic spline interpolation function value of each interpolation node;
s5, finishing compensation machining according to the optimal cutter machining path obtained in the step S4, and detecting machining errors of the machining compensation surface by using an on-machine detection system:
1) if the maximum value of the machining error falls into the tolerance range, stopping compensation machining, and finishing machining of the workpiece;
2) and if the maximum value of the machining error exceeds the tolerance range, repeating the steps S2-S4 until the maximum value of the machining error falls within the tolerance range.
Claims (4)
1. A thin-wall part machining error compensation method based on a mirror image method and cubic spline interpolation is characterized by comprising the following steps:
s1, processing the initial blank until a certain margin is left;
s2, using the on-machine detection system to detect the machining error e of the workpiece surface according to a certain sampling point sequence on the workpiece surface after the step S1k＝{ek1、ek2、…、eknAnd calculating the actual cutting depth value y of the corresponding sampling point sequencek＝{yk1、yk2、…、ykn}；
S3, establishing an optimized error compensation model based on a mirror image method:
s301, substituting machining errors and actual cutting depth values of the n sampling points obtained in the step S2 into a compensation coefficient alphakThe calculation formula of (2):
obtaining the compensation coefficient alpha of n sampling points ═ ak1、ak2、…、akn}; wherein x iskIn order to perform step S1, n sampling points are used to obtain the nominal cutting depth, x, of the previous cutting processk＝{xk1、xk2、…、xkn}；
S302, substituting the compensation coefficient alpha into a mirror image method compensation formula:
xk+1＝xk+αk·ekthe compound of the formula (2),
carrying out error compensation optimization to obtain the nominal cutting depth x in the next compensation processingk+1＝{xk1+1、xk2+1、…、xkn+1}；
S4, the nominal cutting depth x of the n sampling points obtained in the step S3 in the next compensation machiningk+1As an interpolation node, generating a limited number of interpolation points according to the size of an interpolation interval by utilizing a cubic spline interpolation method so as to obtain an optimal tool machining path;
the specific steps of step S4 are:
s401, the n nominal cutting depths x obtained in the step S3k+1As a given interpolation node, where a ═ xk1+1<xk2+1<…<xkn+1＝b，[a,b]Is an interpolation interval;
s402, substituting the interpolation node into an interpolation function equation:
Si(x)＝ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3the compound of the formula (3),
wherein, in formula (3), ai、bi、ciAnd diIs constant, i ═ {0, 1, …, n }; the cubic spline interpolation function is a polynomial not more than cubic, the second order of which is conductive and continuous, and x of the boundary interpolation node of the interpolation intervalkn+1And xkn+1The first derivative values are equal, and the second derivative value is 0;
s403, establishing an equation set according to the boundary conditions of the interpolation function, and performing simultaneous solution to obtain cubic spline interpolation function values of the n interpolation nodes;
s5, finishing compensation machining according to the optimal cutter machining path obtained in the step S4, and detecting machining errors of the machining compensation surface by using an on-machine detection system:
1) if the maximum value of the machining error falls into the tolerance range, stopping compensation machining, and finishing machining of the workpiece;
2) and if the maximum value of the machining error exceeds the tolerance range, repeating the steps S2-S4 until the maximum value of the machining error falls within the tolerance range.
2. A thin-wall part machining error compensation method based on a mirror image method and cubic spline interpolation according to claim 1, wherein in step S1, the machining allowance of an initial blank is 2-3 mm.
3. A thin-wall part machining error compensation method based on a mirror image method and cubic spline interpolation according to claim 1, wherein in step S2, the setting principle of the sampling points is as follows: and setting a sampling point at every interval of 5-10 mm.
4. A thin-wall part machining error compensation method based on a mirror image method and cubic spline interpolation according to claim 1, wherein in step S4, 1-3 difference points are generated between every two interpolation nodes.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910026178.6A CN109765843B (en) | 2019-01-11 | 2019-01-11 | Thin-wall part machining error compensation method based on mirror image method and cubic spline interpolation |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910026178.6A CN109765843B (en) | 2019-01-11 | 2019-01-11 | Thin-wall part machining error compensation method based on mirror image method and cubic spline interpolation |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109765843A CN109765843A (en) | 2019-05-17 |
| CN109765843B true CN109765843B (en) | 2021-06-25 |
Family
ID=66453811
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910026178.6A Active CN109765843B (en) | 2019-01-11 | 2019-01-11 | Thin-wall part machining error compensation method based on mirror image method and cubic spline interpolation |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109765843B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113102882B (en) * | 2021-06-16 | 2021-08-24 | 杭州景业智能科技股份有限公司 | Geometric error compensation model training method and geometric error compensation method |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101377410A (en) * | 2008-10-10 | 2009-03-04 | 哈尔滨工业大学 | Large caliber aspheric surface measuring apparatus and method based on ultra-precise revolving scanning |
| CN107272580A (en) * | 2017-06-15 | 2017-10-20 | 大连理工大学 | A kind of hard brittle material thin-walled parts machining error compensating method |
| CN107479499A (en) * | 2017-09-29 | 2017-12-15 | 西北工业大学 | Thin-wall part cuts interface mismachining tolerance compensating Modeling and penalty coefficient learning control method |
| JP2018200693A (en) * | 2017-05-29 | 2018-12-20 | 株式会社ナガセインテグレックス | Work processing method and work processor |
-
2019
- 2019-01-11 CN CN201910026178.6A patent/CN109765843B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101377410A (en) * | 2008-10-10 | 2009-03-04 | 哈尔滨工业大学 | Large caliber aspheric surface measuring apparatus and method based on ultra-precise revolving scanning |
| JP2018200693A (en) * | 2017-05-29 | 2018-12-20 | 株式会社ナガセインテグレックス | Work processing method and work processor |
| CN107272580A (en) * | 2017-06-15 | 2017-10-20 | 大连理工大学 | A kind of hard brittle material thin-walled parts machining error compensating method |
| CN107479499A (en) * | 2017-09-29 | 2017-12-15 | 西北工业大学 | Thin-wall part cuts interface mismachining tolerance compensating Modeling and penalty coefficient learning control method |
Non-Patent Citations (2)
| Title |
|---|
| 航空薄壁件数控加工变形主动补偿研究;黄晓明，张阁;《滨州学院学报》;20161230(第6期);全文 * |
| 薄壁件加工变形预测及主动补偿方法;张攀,陈蔚芳;《现代制造工程》;20080330(第3期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109765843A (en) | 2019-05-17 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Pham et al. | Micro-EDM—recent developments and research issues | |
| Klocke et al. | Interdisciplinary modelling of the electrochemical machining process for engine blades | |
| Ratchev et al. | An advanced FEA based force induced error compensation strategy in milling | |
| Feng et al. | Constant scallop-height tool path generation for three-axis sculptured surface machining | |
| CN102865847B (en) | Spline curve compensation method for measuring profile deviation based on path unit | |
| CN105242637A (en) | Aviation thin-wall blade compensation processing method | |
| CN102059583B (en) | Finish machining method for large parts difficult to cut | |
| CN106873522B (en) | A kind of numerical control turning cutter path planing method of non-axis symmetry sweeping surface | |
| CN102581705B (en) | Division compensation method for machining error during milling of workpiece | |
| TW201341105A (en) | Lens shape machining method and lens shape machining device for carrying out measurement along spiral measurement path | |
| CN108581635B (en) | Three-dimensional detection device and method for abrasion of side edge of milling cutter | |
| Li et al. | Modeling and application of process damping in milling of thin-walled workpiece made of titanium alloy | |
| CN111266803B (en) | Processing method of thin-wall special-shaped metal casting | |
| Fomin | Limiting product surface and its use in profile milling design operations | |
| CN109765843B (en) | Thin-wall part machining error compensation method based on mirror image method and cubic spline interpolation | |
| CN111077846B (en) | Thin-wall blade allowance removal sequence planning method | |
| CN104317246A (en) | Method for carrying out cutter back-off compensation on multi-shaft processing path of weak-rigidity cutter | |
| Zuo et al. | Integrated geometric error compensation of machining processes on CNC machine tool | |
| Ge et al. | On-machine measurement-based compensation for machining of thin web parts | |
| Bolar et al. | Experimental investigation on surface quality and dimensional accuracy during curvilinear thin-wall machining | |
| Kang et al. | Maximum free distance method for electrode feeding path planning in EDM machining of integral shrouded blisks | |
| Ding et al. | CNC electrical discharge rough machining of turbine blades | |
| Zhang et al. | A novel force-based two-dimensional tool centre error identification method in single-point diamond turning | |
| CN110727246A (en) | Tool and workpiece instantaneous contact contour extraction method based on tool position file | |
| Niesłony et al. | FEM-based optimization of machining operations of aerospace parts made of Inconel 718 superalloy |
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 |