CN105759726B - Adaptive curve interpolating method based on profile errors constraint - Google Patents
Adaptive curve interpolating method based on profile errors constraint Download PDFInfo
- Publication number
- CN105759726B CN105759726B CN201610167558.8A CN201610167558A CN105759726B CN 105759726 B CN105759726 B CN 105759726B CN 201610167558 A CN201610167558 A CN 201610167558A CN 105759726 B CN105759726 B CN 105759726B
- Authority
- CN
- China
- Prior art keywords
- curve
- value
- constraint
- feeding speed
- adaptive
- 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.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims abstract description 36
- 230000003044 adaptive effect Effects 0.000 title claims abstract description 16
- 238000012545 processing Methods 0.000 claims abstract description 26
- 238000003754 machining Methods 0.000 claims abstract description 24
- 238000004364 calculation method Methods 0.000 claims abstract description 8
- 238000013016 damping Methods 0.000 claims description 9
- 238000005316 response function Methods 0.000 claims description 2
- 238000012546 transfer Methods 0.000 claims description 2
- 238000005516 engineering process Methods 0.000 abstract description 4
- 230000036461 convulsion Effects 0.000 description 3
- 210000000988 bone and bone Anatomy 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 230000001133 acceleration Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000002401 inhibitory effect Effects 0.000 description 1
- 238000007747 plating Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
Classifications
-
- 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
- G05B19/41—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 interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
- G05B19/4103—Digital interpolation
-
- 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
- G05B2219/34—Director, elements to supervisory
- G05B2219/34096—Approximate, replace curve, surface with circle, linear segments, least error
Landscapes
- Engineering & Computer Science (AREA)
- Computing Systems (AREA)
- Theoretical Computer Science (AREA)
- Human Computer Interaction (AREA)
- Manufacturing & Machinery (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Numerical Control (AREA)
Abstract
Adaptive curve interpolating method of the present invention based on profile errors constraint belongs to precise high-efficiency Computerized Numerical Control processing technology field, more particularly to a kind of parametric spline curve interpolation feed speed Adaptive Planning method based on profile errors constraint.This method is first against typical second order feed servo-system, association relation model between profile errors and feed speed, servo parameter, curvature of curve is established, is calculated using current interpolated point curvature information and profile errors binding occurrence and processes feed speed allowable value at current interpolated point under profile errors constraint；Secondly, judge that the feed speed and program allowable of profile errors constraint preset feed speed magnitude relationship, using smaller value as the point self-adapted feed speed value of current interpolation；Finally, the parameter of curve of next interpolated point is calculated using the adaptive feed speed, realizes the parametric curve interpolator for taking into account profile errors constraint.Amount of calculation of the present invention is small, practical, can effectively improve curve interpolating machining locus contour accuracy.
Description
Technical Field
The invention belongs to the technical field of precise and efficient numerical control machining, and particularly relates to a parameter spline curve interpolation feed speed self-adaptive planning method based on contour error constraint.
Background
With the rapid development of the fields of aerospace, energy power and other heavy engineering, the requirements of the manufacturing industry on the processing precision and the processing efficiency of the high-end equipment complex curved surface heavy parts are increasingly improved. In view of the fact that the parameter spline curve can accurately represent any free-form curve tool path, approximation errors generated in the process of replacing the curve tool path by a tiny straight line and an arc segment are overcome, and therefore machining accuracy of the curved surface is improved, the parameter curve interpolation technology is widely concerned in the field of high-end numerical control. In the interpolation of the parameter curve, the feed speed is planned as important. The existing curve interpolation speed planning method mainly takes geometric (namely, bow height error) constraint and kinematic (namely, acceleration and jerk) constraint as main constraints, and does not consider profile error constraint induced by the servo hysteresis characteristic of a feed system. Therefore, when the machining feeding speed is high and the curvature of the tool path curve is large, a large machining profile error is easily caused, and the machining precision of the part is reduced. In conclusion, the research of the parameter curve adaptive interpolation technology considering the contour error constraint has important significance for realizing the precise and efficient machining of the complex curved surface part.
Summary of the prior art documents, the document "Cubic bolt Trajectory Generation with Axis Jerk and Tracking Error Constraints", ke Zhang et al, international Journal of Precision Engineering and Manufacturing,2013, 14 (7): 1141-1146, generates C-Spline toolpaths with the feed Axis Jerk and follow-up Error as constraint conditions, and limits the uniaxial follow-up Error in actual machining within the preset Error limit. Although the method can effectively reduce the follow-up error, the follow-up error is not directly related to the machining contour error, and the reduction of the follow-up error does not represent the reduction of the contour error. The documents "Smooth fed plating for connecting short line with connecting error constraint", jingchuan Dong et al, international Journal of Machine Tools and Manual, 2014, 76:1-12, which proposes a method for planning a feeding speed with contour error constraint, but the document simplifies a feeding shaft servo system into a first-order system for discussion, and the simplification degree is too high, which may cause the response of the simplified system to the original system at a higher frequency to be inconsistent.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a self-adaptive curve interpolation method based on contour error constraint.
The technical scheme of the invention is a self-adaptive curve interpolation method based on contour error constraint, which is characterized in that the method firstly establishes an incidence relation model between contour error and feed speed, servo system parameters and curve curvature aiming at a typical second-order feed servo system, and calculates a machining feed speed allowable value at a current interpolation point under the contour error constraint by utilizing current interpolation point curvature information and a contour error constraint value; secondly, judging the relation between the allowable feeding speed of the contour error constraint and the preset feeding speed of the program, and taking a smaller value as the self-adaptive feeding speed value of the current interpolation point; finally, calculating curve parameters of the next interpolation point by utilizing the self-adaptive feeding speed, and realizing the parametric curve interpolation considering the contour error constraint; the method comprises the following specific steps:
allowable machining feed speed calculation under first-step contour error constraint
The closed-loop transfer function G(s) of a typical position closed-loop feed servo system controlled by a proportional controller is:
wherein K is the gain of the position loop proportional controller, J is the equivalent moment of inertia of the load such as the servo motor and the lead screw, B is the equivalent viscous damping of the load, and s is a Laplace operator;
order toEquation (1) can be expressed as a typical second order system:
wherein, ω is n Zeta is the damping ratio for undamped natural frequency; let s = j ω, the frequency response function G (j ω) of the system is obtained as:
wherein, omega is the system input angular frequency;
therefore, the amplitude-frequency characteristic function M (ω) and the phase-frequency characteristic function Φ (ω) of the system are:
when a contour with a curvature radius rho is machined by adopting a feeding speed v, each shaft of a numerical control system inputs a command r x 、r y Comprises the following steps:
wherein the angular frequency ω = v/ρ, (r) x,0 ,r y,0 ) Is the center of a curvature circle; when reaching steady state, each shaft of the system outputs p x 、p y Comprises the following steps:
when the dynamic characteristics of each axis servo system are well matched, M x (ω)＝M y (ω) = M (ω), and the curvature radius of the actually processed contour is M (ω) times the ideal curvature radius, and the contour error ∈ can be expressed as:
ε＝ρ|1-M(ω)| (8)
for a numerical control system, when a control parameter is debugged, the damping ratio ζ is often adjusted to be between 0.707 and 1.0 to ensure good damping characteristic of a servo system; as can be seen from equation (4), when ζ >0.707, M (ω) <1 is present for any ω >0, and therefore equation (8) can be rewritten as:
ε＝ρ(1-M(ω)) (9)
since M (ω) is constantly larger than 0, it can be seen from equation (9) that the maximum value ε of the profile error is obtained when a profile having a curvature radius ρ is machined max Less than rho; thus, for a given profile error limit a constraint value ε lim When is said lim When the speed is not less than rho, the machining feeding speed can meet the requirement no matter how large, and the speed does not need to be planned; when epsilon lim &When the value is lt rho, the equation is solved
Obtaining the angular frequency omega meeting the constraint condition of the profile error c Value, and then obtaining the maximum allowable value v of the processing feed speed satisfying the contour error constraint c ＝ρω c ；
The unique analytical solution of equation (10) is solved below; let Q =1- ε lim /ρ，W＝ω 2 Equation (10) becomes:
obtaining by solution:
due to zeta>, 0.707, (1-2 ζ) 2 )<, 0, and W = ω 2 >, 0, so that:
i.e. solution omega of the equation c Comprises the following steps:
will omega c ＝v c /ρ，Q＝1-ε lim Substituting the rho into the formula to obtain the contour error epsilon lim Maximum allowable machining feed speed value v under constraint c Comprises the following steps:
second step processing feed speed adaptive value calculation
On the basis of obtaining the curve curvature at the current interpolation point, the maximum allowable processing feeding speed under the contour error constraint is calculated by adopting a first-step method, the maximum allowable processing feeding speed is compared with a program preset processing feeding speed value, and the smaller one is selected as a processing feeding speed adaptive value v of the contour error constraint at the current interpolation point i ：
v i ＝min{v c ,v p } (16)
Wherein v is p Presetting a processing feed speed value for a program;
third step interpolation parameter calculation
According to the profile error obtained in the second step, the self-adaptive value v of the feeding speed is restricted i Calculating the curve parameter u at the next interpolation point of the parameter spline curve by using a second-order Taylor series expansion method i+1 ：
Wherein u is i For the current interpolation point curve parameter value, C' (u) i ) First order loss of spline curve, C' (u) at current interpolation point i ) The second-order loss of the spline curve at the current interpolation point is shown, and Ts is an interpolation period;
judging whether a track end point is reached, if the track end point is not reached, enabling i = i +1, and repeating the process; and if the end point is reached, terminating the interpolation, thereby realizing the adaptive curve interpolation considering the contour error constraint.
The beneficial effects of the invention are: a maximum allowable machining feed speed model under the constraint of profile errors is established, and an important reference is provided for feed speed planning in the numerical control interpolation process; the dynamic characteristic of a feeding servo system is fully considered during the interpolation of the parameter curve, and the method has important significance for the precise and efficient machining of complex curved surface parts.
Drawings
FIG. 1 is a general flowchart of an adaptive curve interpolation method based on contour error constraints;
FIG. 2 is a geometric model diagram of a non-uniform rational B-spline curve of a bone shape;
FIG. 3 is a comparison graph of contour error of a processing track by the method and a constant speed curve interpolation method; wherein, the A axis represents spline curve parameters, the B axis represents an absolute value of the profile error, the unit is mm, the curve 1 is a constant speed curve interpolation processing track profile error value, and the curve 2 is a processing track profile error value of the method.
Detailed Description
The detailed description of the invention is provided with reference to the technical scheme and the attached drawings.
In the interpolation process of the parameter spline curve, if the dynamic characteristic of a machine tool is not considered, the profile error is easily generated when the feeding speed is high and the curvature of a processing track is high, and the processing precision of the curved surface part is influenced. Therefore, the invention provides the self-adaptive curve interpolation method based on the contour error constraint.
Taking non-uniform rational B-spline curve interpolation as an example, the implementation process of the invention is explained in detail by calculation and simulation of MATLAB software, and the whole flow is shown in attached figure 1.
First, as shown in fig. 1, first, let i =1, i be the current interpolation point number, and calculate the curvature radius ρ of the curve at the current interpolation point:
in this example, the interpolation locus is a "bone" shaped curve, the geometric model is shown in fig. 2, and the curve parameters are: the order is as follows: 2; and (3) control points: { (0, 0); (-8, -20); (30, -5); (60, -20); (47, 0); (60, 20); (30, 5); (-8,20); (0, 0) }; the weight factor is: {1,0.9,0.75,1.5,6,3.5,1.8,1.5,1}; and (3) node vector: {0, 0.15,0.3,0.45,0.6,0.75,0.85, 1};
secondly, the curvature radius rho of the curve of the current interpolation point and the parameter omega of the servo system of the feed shaft are calculated n ζ, contour error limit constraint values ε lim Substituting the formula (15) into the above formula to obtain the maximum allowable machining feed speed value v under the constraint of the profile error at the current interpolation point c (ii) a Further, according to the formula (16), the adaptive feed speed value v at the current interpolation point is calculated i ；
In this example, the undamped natural frequency ω is taken n =67.08 (1/s), damping ratio ζ =0.745, contour error limit constraint value ∈ lim =0.01mm, preset feed speed v p ＝80(mm/s)；
Thirdly, self-adapting the feed speed value v according to the current interpolation point i Calculating the curve parameter u at the next interpolation point by the formula (17) i+1 (ii) a In this example, an interpolation period Ts =0.002s; judging whether a track end point is reached, if the track end point is not reached, enabling i = i +1, and repeating the process; if the end point is reached, terminating the interpolation;
for the bone-shaped curve in the present example, the above steps are adopted to perform adaptive interpolation of parameter spline curve, and the comparison between the contour error of the obtained processing track wheel and the contour error of the processing track obtained by constant-speed curve interpolation is shown in fig. 3; as can be seen from the attached figure 3, by adopting the method, the processing contour error can be effectively inhibited, and the precision of the parameter curve interpolation processing contour is improved.
Aiming at the problem that the profile error of a large-curvature machining track is large due to the dynamic characteristic of a machine tool when a parameter curve is interpolated at a high feeding speed, the invention discloses an adaptive curve interpolation method based on profile error constraint, which is used for inhibiting the profile error of the curve interpolation machining track and has great significance on the development of numerical control technology and the precise and efficient machining of high-performance complex curved surface parts.
Claims (1)
1. A self-adaptive curve interpolation method based on contour error constraint is characterized in that the method firstly establishes an incidence relation model between contour error and feeding speed, servo system parameters and curve curvature aiming at a typical second-order feeding servo system, and calculates a machining feeding speed allowable value at a current interpolation point under the contour error constraint by utilizing the curvature information of the current interpolation point and a contour error constraint value; secondly, judging the relation between the allowable feeding speed of the contour error constraint and the preset feeding speed of the program, and taking a smaller value as the self-adaptive feeding speed value of the current interpolation point; finally, calculating curve parameters of a next interpolation point by using the self-adaptive feeding speed, and realizing parameter curve interpolation considering contour error constraint; the method comprises the following specific steps:
allowable machining feed speed calculation under first-step contour error constraint
The closed loop transfer function G(s) of a typical position closed loop feed servo controlled by a proportional controller is:
k is the gain of the position ring proportional controller, J is the equivalent moment of inertia of the servo motor and the lead screw load, B is the equivalent viscous damping of the load, and s is a Laplace operator;
order toEquation (1) is then expressed as a typical second order system:
wherein, ω is n Zeta is the damping ratio for undamped natural frequency; let s = j ω, the frequency response function G (j ω) of the system is obtained as:
wherein, omega is the system input angular frequency;
therefore, the amplitude-frequency characteristic function M (ω) and the phase-frequency characteristic function Φ (ω) of the system are respectively:
when a profile with a curvature radius rho is machined by adopting a feeding speed v, an instruction r is input into each shaft of the numerical control system x 、r y Comprises the following steps:
wherein the angular frequency ω = v/ρ, (r) x,0 ,r y,0 ) Is the center of a curvature circle; when reaching steady state, each shaft of the system outputs p x 、p y Comprises the following steps:
when the dynamic characteristics of each axis servo system are well matched, M x (ω)＝M y (ω) = M (ω), and the radius of curvature of the actual machining profile is M (ω) times the ideal radius of curvature, and the profile error ∈ when:
ε＝ρ|1-M(ω)| (8)
for a numerical control system, when a control parameter is debugged, the damping ratio zeta is usually adjusted to be between 0.707 and 1.0 to ensure good damping characteristic of a servo system; when ζ >0.707 by the formula (4), M (ω) <1 is present for any ω >0, and therefore the formula (8) is rewritten as:
ε＝ρ(1-M(ω)) (9)
since M (ω) is constantly larger than 0, the maximum value ε of the profile error is obtained by the equation (9) when a profile having a curvature radius ρ is machined max Less than rho; thus, the limit constraint value ε is given the profile error lim When epsilon lim When the speed is not less than rho, the machining feeding speed can meet the requirement no matter how large, and the speed does not need to be planned; when epsilon lim &When lt rho, by solving the equation
Obtaining the angular frequency omega meeting the constraint condition of the profile error c Value, and then obtaining the maximum allowable value v of the processing feed speed satisfying the contour error constraint c ＝ρω c ；
The following solves a unique analytical solution of equation (10); let Q =1- ε lim /ρ，W＝ω 2 Equation (10) becomes:
obtaining by solution:
due to zeta>, 0.707, (1-2 ζ) 2 )<, 0, and W = ω 2 >, 0, so that:
i.e. solution omega of the equation c Comprises the following steps:
will omega c ＝v c /ρ，Q＝1-ε lim Substituting the rho into the formula to obtain the contour error epsilon lim Maximum allowable machining feed speed value v under constraint c Comprises the following steps:
second step processing feed speed adaptive value calculation
On the basis of obtaining the curve curvature at the current interpolation point, the maximum allowable processing feeding speed under the contour error constraint is calculated by adopting a first-step method, the maximum allowable processing feeding speed is compared with a program preset processing feeding speed value, and the smaller one is selected as a processing feeding speed adaptive value v of the contour error constraint at the current interpolation point i ：
v i ＝min{v c ,v p } (16)
Wherein v is p Presetting a processing feeding speed value for a program;
third step of interpolation parameter calculation
According to the profile error obtained in the second step, the self-adaptive value v of the feeding speed is restricted i Calculating the curve parameter value u at the next interpolation point of the parameter spline curve by using a second-order Taylor series expansion method i+1 ：
Wherein u is i For the current interpolation point curve parameter value, C' (u) i ) First order loss of spline curve, C' (u) at current interpolation point i ) The second-order loss of the spline curve at the current interpolation point is shown, and Ts is an interpolation period;
judging whether a track end point is reached, if the track end point is not reached, enabling i = i +1, and repeating the first step to the third step of the process; and if the end point is reached, terminating the interpolation, thereby realizing the adaptive curve interpolation considering the contour error constraint.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610167558.8A CN105759726B (en) | 2016-03-22 | 2016-03-22 | Adaptive curve interpolating method based on profile errors constraint |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610167558.8A CN105759726B (en) | 2016-03-22 | 2016-03-22 | Adaptive curve interpolating method based on profile errors constraint |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105759726A CN105759726A (en) | 2016-07-13 |
| CN105759726B true CN105759726B (en) | 2018-04-10 |
Family
ID=56346144
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610167558.8A Expired - Fee Related CN105759726B (en) | 2016-03-22 | 2016-03-22 | Adaptive curve interpolating method based on profile errors constraint |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105759726B (en) |
Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106200553B (en) * | 2016-08-03 | 2018-07-13 | 大连理工大学 | It is servo-actuated to cooperate with compensation method online with profile errors |
| CN107291047B (en) * | 2017-07-14 | 2020-02-07 | 福建工程学院 | Positive and negative bidirectional NURBS curve interpolation method based on multiple constraint conditions |
| CN108445832B (en) * | 2018-02-23 | 2020-12-29 | 陕西丰赜机电科技有限公司 | Method for generating and processing follow-up grinding cutter track and arc splicing numerical control program |
| CN110989503A (en) * | 2019-11-29 | 2020-04-10 | 华中科技大学 | Method for controlling milling feeding speed of cutter relieving error constraint complex curved surface |
| CN113341886B (en) * | 2021-05-25 | 2022-12-27 | 深圳市汇川技术股份有限公司 | Smooth feed speed planning method, device and computer readable storage medium |
| CN113554649B (en) * | 2021-09-22 | 2021-12-17 | 中科慧远视觉技术(北京)有限公司 | Defect detection method and device, computer equipment and storage medium |
| CN114740800B (en) * | 2022-03-09 | 2024-05-24 | 天津大学 | Double-sliding-mode direct contour control method of parameter curve processing path |
| CN115128996A (en) * | 2022-07-04 | 2022-09-30 | 深圳市汇川技术股份有限公司 | Error compensation method, device, equipment and medium for numerical control machining |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4754208A (en) * | 1986-11-17 | 1988-06-28 | Nippon Kokan Kabushiki Kaisha | Circular path control apparatus and method for multi-axis servomechanisms |
| EP0413825A1 (en) * | 1989-03-13 | 1991-02-27 | Fanuc Ltd. | Involute-interpolation speed control method |
| CN102419570A (en) * | 2011-09-29 | 2012-04-18 | 上海大学 | Acceleration and deceleration look-ahead control method for high-speed machining of numerical control machine tool |
| CN102681489A (en) * | 2012-06-01 | 2012-09-19 | 南京航空航天大学 | Control method for motion stability and outline machining precision of multi-shaft linkage numerical control system |
| CN104615084A (en) * | 2015-01-23 | 2015-05-13 | 大连理工大学 | Machining feed speed optimized tool path curve contour error compensation method |
| CN104615083A (en) * | 2015-01-23 | 2015-05-13 | 大连理工大学 | Curved surface tool path contour error compensation method based tool location point correction |
| CN104898564A (en) * | 2015-05-04 | 2015-09-09 | 大连理工大学 | Method for reducing three-shaft linkage contour error |
-
2016
- 2016-03-22 CN CN201610167558.8A patent/CN105759726B/en not_active Expired - Fee Related
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4754208A (en) * | 1986-11-17 | 1988-06-28 | Nippon Kokan Kabushiki Kaisha | Circular path control apparatus and method for multi-axis servomechanisms |
| EP0413825A1 (en) * | 1989-03-13 | 1991-02-27 | Fanuc Ltd. | Involute-interpolation speed control method |
| CN102419570A (en) * | 2011-09-29 | 2012-04-18 | 上海大学 | Acceleration and deceleration look-ahead control method for high-speed machining of numerical control machine tool |
| CN102681489A (en) * | 2012-06-01 | 2012-09-19 | 南京航空航天大学 | Control method for motion stability and outline machining precision of multi-shaft linkage numerical control system |
| CN104615084A (en) * | 2015-01-23 | 2015-05-13 | 大连理工大学 | Machining feed speed optimized tool path curve contour error compensation method |
| CN104615083A (en) * | 2015-01-23 | 2015-05-13 | 大连理工大学 | Curved surface tool path contour error compensation method based tool location point correction |
| CN104898564A (en) * | 2015-05-04 | 2015-09-09 | 大连理工大学 | Method for reducing three-shaft linkage contour error |
Non-Patent Citations (1)
| Title |
|---|
| 基于动态轮廓误差的微段速度规划并行算法;方晨曦等;《计算机集成制造***》;20140630;第20卷(第6期);第1359-1366页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105759726A (en) | 2016-07-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105759726B (en) | Adaptive curve interpolating method based on profile errors constraint | |
| Weck et al. | Sharp corner tracking using the IKF control strategy | |
| US20200004228A1 (en) | A feedrate scheduling method for five-axis dual-spline curve interpolation | |
| Lo | Real-time generation and control of cutter path for 5-axis CNC machining | |
| CN110601624B (en) | Servo control device | |
| Chen et al. | Contour error–bounded parametric interpolator with minimum feedrate fluctuation for five-axis CNC machine tools | |
| He et al. | A tolerance constrained G2 continuous path smoothing and interpolation method for industrial SCARA robots | |
| Du et al. | An accurate adaptive parametric curve interpolator for NURBS curve interpolation | |
| Sun et al. | An on-line tool path smoothing algorithm for 6R robot manipulator with geometric and dynamic constraints | |
| Chen et al. | Adaptive feedrate planning for continuous parametric tool path with confined contour error and axis jerks | |
| CN115113582B (en) | Part contour error-oriented five-axis position loop gain off-line correction method | |
| Xi et al. | Experimental implementation of Taylor series expansion error compensation on a bi-axial CNC machine | |
| CN105005265A (en) | Numerical control machining feed rate programming method based on curve smooth deformation | |
| Duong et al. | Contour error pre-compensation for five-axis high speed machining: offline gain adjustment approach | |
| CN105717874B (en) | A kind of five-shaft numerical control processing singular regions cutter location optimization method | |
| Jia et al. | Adaptive estimation and nonlinear variable gain compensation of the contouring error for precise parametric curve following | |
| Yang et al. | A two-stage CNC interpolation algorithm for corner smoothing trajectories with geometric error and dynamics constraints | |
| CN111033404B (en) | Method for operating a numerically controlled machine tool and associated machine tool | |
| Shi et al. | A novel contouring error estimation for three-dimensional contouring control | |
| Simba et al. | Bézier curve based trajectory generation and nonlinear friction compensation for feed drive contouring control | |
| Cheng et al. | Feedrate control for non-uniform rational B-spline motion command generation | |
| Wang et al. | Research and implementation of high-precision biaxial tracking control system based on NURBS interpolator | |
| Geng et al. | A tool path correction and compression algorithm for five-axis CNC machining | |
| Xu et al. | Variable feedrate CNC interpolation for planar implicit curves | |
| Zhao et al. | An adaptive feedrate scheduling method with multi-constraints for five-axis machine tools |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20180410 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |