CN114035504B - Acceleration and deceleration control method based on time optimization, numerical control system, medium and machine tool - Google Patents
Acceleration and deceleration control method based on time optimization, numerical control system, medium and machine tool Download PDFInfo
- Publication number
- CN114035504B CN114035504B CN202111305713.5A CN202111305713A CN114035504B CN 114035504 B CN114035504 B CN 114035504B CN 202111305713 A CN202111305713 A CN 202111305713A CN 114035504 B CN114035504 B CN 114035504B
- Authority
- CN
- China
- Prior art keywords
- max
- maximum
- acceleration
- jerk
- 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.)
- Active
Links
- 230000001133 acceleration Effects 0.000 title claims abstract description 264
- 238000000034 method Methods 0.000 title claims abstract description 90
- 238000005457 optimization Methods 0.000 title abstract description 4
- 230000036461 convulsion Effects 0.000 claims abstract description 150
- 238000003754 machining Methods 0.000 claims abstract description 42
- 230000008569 process Effects 0.000 claims abstract description 30
- 238000006073 displacement reaction Methods 0.000 claims description 22
- 230000008859 change Effects 0.000 claims description 7
- 238000004590 computer program Methods 0.000 claims description 2
- 238000003860 storage Methods 0.000 claims description 2
- BULVZWIRKLYCBC-UHFFFAOYSA-N phorate Chemical compound CCOP(=S)(OCC)SCSCC BULVZWIRKLYCBC-UHFFFAOYSA-N 0.000 claims 1
- 238000004519 manufacturing process Methods 0.000 abstract description 7
- 230000006870 function Effects 0.000 description 20
- 238000003801 milling Methods 0.000 description 4
- 230000007547 defect Effects 0.000 description 3
- 230000006978 adaptation Effects 0.000 description 2
- 238000009795 derivation Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000035772 mutation Effects 0.000 description 1
- 230000008092 positive effect Effects 0.000 description 1
- 230000000007 visual effect Effects 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
- G05B19/19—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 positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
-
- 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
- G05B2219/35—Nc in input of data, input till input file format
- G05B2219/35349—Display part, programmed locus and tool path, traject, dynamic locus
Landscapes
- Engineering & 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
The invention belongs to the technical field of numerical control in mechanical manufacturing engineering, and discloses an acceleration and deceleration control method, a numerical control system, a medium and a machine tool based on time optimization. Dividing the machining process of the numerical control system into a plurality of sections, and analyzing the conditions of maximum jerk, maximum acceleration and maximum speed in the machining process according to the movement conditions of numerical control machining; and analyzing whether each stage of the processing process exists according to the processing conditions so as to obtain the running time of each stage of the processing process and further obtain a motion curve after the processing speed planning. Compared with the existing trigonometric function acceleration and deceleration control method, the method has the advantages that smooth and continuous acceleration and jerk curves are realized, but compared with the trigonometric function acceleration and deceleration, the method can keep the maximum jerk for processing, can more effectively play the motion performance of the numerical control machine tool, and improves the processing efficiency.
Description
Technical Field
The invention belongs to the technical field of numerical control in mechanical manufacturing engineering, and particularly relates to a time-optimal-based continuous acceleration and deceleration control method and system.
Background
At present, the manufacturing industry is an important pillar of national economy, the mechanical manufacturing industry is the core of the manufacturing industry, the numerical control machining has a non-negligible position in the mechanical manufacturing industry, and the numerical control machining has wide application for machining complex parts and the like. In recent years, research on interpolation algorithms of numerical control machining by expert scholars is increasing year by year, and the research of numerical control systems is popular. The acceleration and deceleration control is used as an important component of numerical control interpolation processing, and has important significance for improving the numerical control processing precision and efficiency.
The earliest T-shaped acceleration and deceleration can cause abrupt change of acceleration at the beginning and the end of processing, thereby causing vibration in the processing process and affecting the processing quality. At present, the most used S-shaped acceleration and deceleration has high processing efficiency and continuous acceleration, but the problem of sudden change of jerk in the processing process exists. Trigonometric acceleration and deceleration is good in continuity of jerk during machining as compared with S-type acceleration and deceleration, but slightly lower in machining efficiency than S-type acceleration and deceleration, but for S-type acceleration and deceleration. In the existing research, the acceleration and deceleration algorithm research of continuous acceleration and deceleration proposed in the "acceleration and deceleration algorithm research of continuous acceleration and deceleration [ J ]. Machine manufacturing, 2021" can realize continuous acceleration and deceleration of the proposed sine function, but in the acceleration and deceleration planning process, the maximum acceleration and deceleration only occur in the peak point, the maximum acceleration and deceleration can not be continuously utilized for acceleration or deceleration, and the movement performance of the numerical control machine tool is not fully exerted, so that the machining efficiency is low. Therefore, the triangle function acceleration and deceleration, the acceleration and deceleration curve is smooth, the smoothness of the motion can be ensured, but the processing efficiency is low; the S-type acceleration and deceleration is high in processing efficiency, but smoothness of motion control cannot be ensured.
Through the above analysis, the problems and defects existing in the prior art are as follows:
(1) In the prior art, in the processing control, a numerical control system causes vibration and impact due to sudden change of acceleration or jerk, so that the processing quality is affected.
(2) In the prior art, the numerical control machine tool cannot keep the maximum jerk for processing, and the processing efficiency is low.
The difficulty of solving the problems and the defects is as follows: the acceleration and deceleration of the trigonometric function adopted in the numerical control machining can realize the continuity of the acceleration, but the maximum acceleration only exists on a peak point due to the characteristic of the trigonometric function in the whole machining process, so that the maximum acceleration cannot be fully utilized for acceleration, and the motion performance of the numerical control machine tool cannot be fully utilized. At present, the processing of maintaining the maximum jerk in the acceleration and deceleration of the trigonometric function is less studied, and only the S-shaped acceleration and deceleration can realize the processing of maintaining the maximum jerk, but the jerk is discontinuous, and vibration and impact are caused in the processing. Therefore, in order to achieve processing while maintaining the maximum jerk, it is necessary to analyze and compare the acceleration and deceleration of the trigonometric function and the acceleration and deceleration of the S-type, and to control and analyze the jerk during processing and analyze conditions such as the maximum jerk, the maximum acceleration, and the maximum speed.
The meaning of solving the problems and the defects is as follows: the acceleration and deceleration control method can fully utilize the motion performance of the numerical control machine tool, enhance the acceleration and deceleration efficiency of the numerical control machining while ensuring the acceleration and deceleration continuity of the numerical control machining, reduce the vibration and impact in the numerical control machining and effectively improve the numerical control machining efficiency.
Disclosure of Invention
In order to overcome the problems in the related art, the embodiment of the invention provides a continuous acceleration and deceleration control method based on time optimal jerk. In particular to a continuous acceleration and deceleration control method based on time optimal jerk.
The technical scheme is as follows: a continuous acceleration and deceleration control method based on time optimization is characterized in that a machining process of a numerical control system is divided into 15 sections, the conditions of maximum acceleration, maximum acceleration and maximum speed in the machining process are analyzed according to the motion conditions of numerical control machining, whether each stage exists or not is discussed according to the machining conditions, so that the running time of each stage is obtained, and further a motion curve after speed planning is obtained.
Another object of the present invention is to provide a numerical control system for implementing the time-optimal jerk-based continuous acceleration/deceleration control method, the numerical control system including:
the maximum jerk analysis module is used for analyzing the maximum jerk of a plurality of stages of processing process division according to the motion condition of numerical control processing;
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages of processing process division according to the motion condition of numerical control processing;
the maximum speed analysis module is used for analyzing the maximum speeds of a plurality of stages of machining process division according to the movement conditions of numerical control machining;
and the processing speed motion curve acquisition module is used for analyzing whether each stage of the processing process exists according to the processing conditions so as to obtain the running time of each stage of the processing process and further obtain the motion curve after the processing speed planning.
Another object of the present invention is to provide a storage medium storing a computer program for causing an electronic device to execute the time-optimal jerk-based continuous acceleration/deceleration control method.
Another object of the present invention is to provide a numerical control machine that implements the time-optimal jerk-based continuous acceleration/deceleration control method.
By combining all the technical schemes, the invention has the advantages and positive effects that:
the acceleration and deceleration control method of the invention, the S-shaped acceleration and deceleration method of the prior art and the existing trigonometric function acceleration and deceleration control method are used for processing the same track under the same condition to obtain different acceleration and deceleration curves and processing parameter tables. As can be seen from table 2, compared with the acceleration and deceleration of the trigonometric function, the acceleration and deceleration method provided herein improves the processing efficiency by about 3.8% under the condition that the fluctuation of the acceleration and deceleration is not great; compared with S-type acceleration and deceleration, under the condition that the processing efficiency is not greatly different, the fluctuation of the maximum jerk is reduced by about two orders of magnitude.
Table 1 table of processing parameters
| Initial parameters | Jounce | J max | A max | V max |
| Parameter value | 10 7 mm/s 4 | 5×10 4 mm/s 3 | 1500mm/s 2 | 100mm/s |
Table 2 comparison table of acceleration and deceleration processing
| Acceleration and deceleration control method | Length of processing mm | Processing time ms | Maximum jerk fluctuation mm/s 4 |
| S-shaped acceleration and deceleration method | 86 | 1422.6 | 5×10 7 |
| Trigonometric function acceleration and deceleration square | 86 | 1553.3 | 3.3×10 5 |
| The invention relates to an addition and deceleration method | 86 | 1493.0 | 9×10 5 |
Compared with the existing S-shaped acceleration and deceleration control method, the acceleration curve and the jerk curve are smoother under the condition of small processing efficiency difference, vibration and impact caused by acceleration or jerk mutation in a numerical control system are reduced, and processing quality is improved. Compared with the existing trigonometric function acceleration and deceleration control method, the method has the advantages that smooth and continuous acceleration and jerk curves are realized, but compared with the trigonometric function acceleration and deceleration, the method can keep the maximum jerk for processing, can more effectively play the motion performance of the numerical control machine tool, and improves the processing efficiency.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure of the invention as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the disclosure and together with the description, serve to explain the principles of the disclosure.
Fig. 1 is a flowchart of an acceleration/deceleration control method based on time-optimal jerk continuity according to an embodiment of the present invention.
Fig. 2 is a graph of a 7-segment S-shaped acceleration/deceleration model in the prior art according to an embodiment of the present invention.
In fig. 2: t (T) i Representing the phases t i-1 ～t i (i=1, 2, ·, 7) time, V max For maximum speed during operation, A max For transportingMaximum acceleration during a row, J max For maximum jerk during operation
Fig. 3 is a triangle function type acceleration and deceleration model curve in the prior art provided by the embodiment of the invention.
In fig. 3: t (T) i Representing the phases t i-1 ～t i (i=1, 2, ·, 7) time, V max For maximum speed during operation, A max For maximum acceleration during operation, J max Is the maximum jerk during operation.
Fig. 4 is a graph of a time-optimal jerk-continuous acceleration/deceleration control model provided by the present invention.
In fig. 4: t (T) i Representing the phases t i-1 ～t i (i=1, 2, ·, 15), V max For maximum speed during operation, A max For maximum acceleration during operation, J max Is the maximum jerk during operation.
Fig. 5 is a graph showing the comparison of motion curves of S-shaped acceleration and deceleration, trigonometric function acceleration and deceleration and acceleration and deceleration processing according to the embodiment of the invention.
Fig. 6 is a graph of acceleration and deceleration motion for actual processing according to case 1 provided by an embodiment of the present invention.
Fig. 7 is a graph of acceleration motion for actual processing according to case 2 provided by an embodiment of the present invention.
Fig. 8 is a schematic diagram of a case 3 according to the motion parameters and the processing information of the tri-axial numerically controlled milling machine of case 1, which is provided by the embodiment of the present invention, to make a speed plan of S-type acceleration and deceleration, 7-segment trigonometric function acceleration and deceleration, and continuous acceleration and deceleration based on time-optimal acceleration and deceleration, and to output a second motion graph.
Detailed Description
In order that the above objects, features and advantages of the invention will be readily understood, a more particular description of the invention will be rendered by reference to the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The invention may be embodied in many other forms than described herein and similarly modified by those skilled in the art without departing from the spirit or scope of the invention, which is therefore not limited to the specific embodiments disclosed below.
As shown in fig. 1, the acceleration and deceleration control method based on time-optimal jerk continuous provided by the embodiment of the invention includes:
s101, dividing the machining process of the numerical control system into a plurality of sections;
s102, analyzing the conditions of maximum jerk, maximum acceleration and maximum speed in the machining process according to the motion conditions of numerical control machining;
s103, analyzing whether each stage of the processing process exists according to the processing conditions to obtain the running time of each stage of the processing process, and further obtaining a motion curve after processing speed planning.
The invention also provides a numerical control system for implementing the time-optimal jerk-based continuous acceleration and deceleration control method, the numerical control system comprises:
the maximum jerk analysis module is used for analyzing the maximum jerk of a plurality of stages of processing process division according to the motion condition of numerical control processing;
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages of processing process division according to the motion condition of numerical control processing;
the maximum speed analysis module is used for analyzing the maximum speeds of a plurality of stages of machining process division according to the movement conditions of numerical control machining;
and the processing speed motion curve acquisition module is used for analyzing whether each stage of the processing process exists according to the processing conditions so as to obtain the running time of each stage of the processing process and further obtain the motion curve after the processing speed planning.
The technical scheme of the invention is further described below with reference to specific embodiments.
Examples
As shown in fig. 2, a 7-segment S-shaped acceleration/deceleration model curve in the prior art. In fig. 2: t (T) i Representing the phases t i-1 ～t i (i=1, 2, ·, 7) time, V max For maximum speed during operation, A max For maximum acceleration during operation, J max Is the maximum jerk during operation.
Fig. 3 is a curve of a prior art sine trigonometric function type acceleration and deceleration model. In fig. 3: t (T) i Representing the phases t i-1 ～t i (i=1, 2, ·, 7) time, V max For maximum speed during operation, A max For maximum acceleration during operation, J max Is the maximum jerk during operation.
As shown in fig. 4, the continuous acceleration and deceleration control method based on time-optimal jerk provided by the invention comprises the following steps: the whole movement time of numerical control machining is set as T, and the invention divides the whole machining time into 15 sections which are respectively 0-T 1 ，t 1 ～t 2 ，t 2 ～t 3 ，…，t 14 ～t 15 Defining the time interval of each time period as T i (i=1, 2, ·, 15), then T i The corresponding time period is t i-1 ～t i (i=1, 2, carrying out 15. Wherein 0 to t 7 To accelerate the phase, t 7 ～t 8 At a constant speed, t 8 ～t 15 For the deceleration phase, T 1 For accelerating movement with increased jerk, T 2 For maximum jerk acceleration movement, T 3 For acceleration movement with reduced jerk, T 4 To maintain maximum acceleration of the acceleration movement, T 5 For acceleration movement with reduced jerk, T 6 Acceleration movement with minimum jerk, T 7 For accelerating movement with increased jerk, T 8 For uniform movement, T 9 ～T 15 For decelerating movement, and accelerating process T 1 ～T 7 Symmetrical. Therefore, in the description of the acceleration and deceleration algorithm, an acceleration stage and a constant velocity stage are taken as examples.
To ensure the continuity of jerk, the invention uses sin 2 (x) Calculating as a basis function to obtain an expression j (t) related to jerk in the acceleration/deceleration control method:
wherein J is max Is the maximum jerk during operation.
In a preferred embodiment of the invention, j (t) can be integrated to obtain the expression a (t) of acceleration:
wherein J is max For maximum jerk during operation, a i (i=2, 3, ·, 6) at time t=t i Can be expressed as:
a 2 ＝a 1 +J max ·T 2
a 4 ＝a 3
a 6 ＝a 5 -J max ·T 6
in a preferred embodiment of the present invention, the velocity expression v (t) may be integrated from the acceleration expression a (t):
wherein J is max For maximum jerk during operation, v s V for initial processing speed i (i=2, 3, ·, 6) at time t=t i Is expressed as:
v 4 ＝v 3 +a 3 ·T 4
in a preferred embodiment of the invention, the velocity expression v (t) may be integrated to obtain the displacement expression s (t):
wherein J is max For maximum jerk during operation, v s S is the initial processing speed i (i＝2,3, & 6) is at time t=t i Is expressed as:
s 8 ＝s 7 +v 7 ·T 8
in a preferred embodiment of the present invention, the present invention may be based on the length S of the machining track, the maximum jerk Jounce, and the maximum jerk J max Maximum acceleration A max Maximum speed V max And (5) planning a displacement curve, a speed curve, an acceleration curve and a jerk curve of the whole processing process in real time according to the motion parameters.
(1.1) in the whole process, the invention divides the whole process into 15 sections, and the maximum jerk of the accelerating section and the decelerating section is the same due to the same parameter settingJ max And maximum acceleration A max The same, so the speed accelerates from 0 to maximum speed V max Theoretically the sum speed is from the maximum speed V max The time to slow down to 0 is the same, so the acceleration and deceleration sections are symmetrical over the speed profile, so in the subsequent derivation, T 1 Time of acceleration period, T, indicating increase in jerk 2 Indicating the acceleration period time for maintaining maximum jerk, T 4 The acceleration period time representing the maximum acceleration is maintained:
T 1 ＝T 3 ＝T 5 ＝T 7 ＝T 9 ＝T 11 ＝T 13 ＝T 15 (5)
T 2 ＝T 6 ＝T 10 ＝T 14 (6)
T 4 ＝T 12 (7)
first, the present invention judges whether the maximum jerk J can be reached max To reach J max Acceleration A of (2) 1 Velocity V 1 And displacement S 1 The conditions are as follows:
(2.1) if A max ≥A 1 ，V max ≥V 1 ，S≥S 1
At this time, it is explained that the processing of this section can reach the maximum jerk J max At this time addTime T of acceleration period of increased speed 1 The method comprises the following steps:
next, the present invention also needs to determine whether the maximum acceleration A can be reached max To reach A max Velocity V of (2) 2 And displacement S 2 The conditions are as follows:
V 2 ＝2J max T 1 2 +3J max T 1 T 2 +J max T 2 2 (14)
S 2 ＝2×(4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 ) (15)
(2.1.1) if V max ≥V 2 ,S≥S 2
At this time, it is explained that the processing of this section can reach the maximum acceleration A max And maintains the time T of the maximum jerk acceleration period 2 Also determined is:
wherein A is 1 Is a parameter in the formula (II),
next, it is necessary to determine whether the maximum speed V can be reached max To reach V max Is of the displacement S of (2) 3 The conditions are as follows:
(2.1.1. A) if S.gtoreq.S 3
At this time, it is explained that the present section of processing can reach the maximum speed V max Acceleration period time T for maintaining maximum acceleration 4 The method comprises the following steps:
according to the displacement S and the maximum velocity V max For time T of constant velocity section 8 And (3) carrying out solving:
(2.1.1. B) if S < S 3
At this time, it is explained that the maximum speed V cannot be reached due to the fact that the processing length S of the present segment is too short max Indicating that there is no constant velocity phase (T 8 =0). The formula can be deduced according to the displacement formula, and the acceleration period time T for keeping the maximum acceleration can be obtained by solving the formula 4 .
Maximum speed V achievable at this time 3 Is that
V 3 ＝V 2 +T 4 ·A max (22)
(2.1.2) if V max ＜V 2 ,S≥S 2
At this time, it is explained that the present section processing is due to the maximum speed V max Constraint of conditions, failure to reach maximum acceleration A max . So that the acceleration section maintaining the maximum jerk can be solved according to the following formulaTime T 2 ：
V max ＝2J max T 1 2 +3J max T 1 T 2 +J max T 2 2 (23)
Time T of constant velocity section 8 Expressed as:
wherein S is 4 ＝2×(4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 )。
(2.1.3) if S < S 2
At this time, it is explained that the maximum acceleration A cannot be reached due to the too short working length S max . Deriving the maximum acceleration A achievable from the working length S 3 Judging the maximum speed V currently reached 4 Whether or not the maximum speed V can be satisfied max Conditions.
According to the method, the acceleration period time T for keeping the maximum jerk is solved 2
S＝2×(4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 ) (25)
Solving for the maximum acceleration A according to the working length S 3 And maximum speed V 4 Conditions are as follows:
A 3 ＝J max ·T 1 +J max ·T 2 (26)
V 4 ＝2J max T 1 2 +3J max T 1 T 2 +J max T 2 2 (27)
(2.1.3. A) if V 4 ≥V max
At this time, it is explained that the present section of processing can reach the maximum speed V max But cannot reach the maximum acceleration A max . The acceleration period time T for maintaining maximum jerk can thus be solved from 2 ：
V max ＝2J max T 1 2 +3J max T 1 T 2 +J max T 2 2 (28)
Solving the time T of the constant speed section according to the displacement S 8 ：
Wherein S is 5 ＝2×(4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 )。
(2.1.3. B) if V 4 ＜V max
At the moment, the processing of the section can not reach the maximum acceleration A max And maximum speed V max So the acceleration period time T of the maximum acceleration is maintained 4 And time T of constant velocity section 8 Is 0. Obtaining the acceleration period time T for keeping the maximum jerk according to the solving equation 2 ：
S＝2×(4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 ) (30)
(2.2) if A max ＜A 1 ，V max ≥V 1 ，S≥S 1
At this time, due to the maximum acceleration A max Constraint of conditions, the maximum jerk J cannot be reached in the processing of the section max So the time T of the maximum jerk acceleration period is maintained 2 =0. According to maximum acceleration A max Determining the maximum jerk J that can be achieved 1 ：
Time T of acceleration period of increased jerk 1 Following the maximum jerk change:
in a preferred embodiment of the invention, the invention requires a determination that the maximum speed V can be reached max According to V max The determined displacement condition S 6 ：
(2.2.1) if S > S 6
At this time, it is explained that the working length S is sufficient to reach the maximum speed V max Obtaining the acceleration period time T for maintaining the maximum acceleration 4 And a constant speed period of time T 8 ：
(2.2.2) if S is less than or equal to S 6
At this time, it is explained that, in the present stage of processing, the processing length S is too short to reach the maximum speed V max (T 8 =0). The acceleration period time T for maintaining the maximum acceleration can be obtained by solving the equation 4 ：
(2.3) if A max ≥A 1 ，V max ＜V 1 ，S≥S 1
At this time, due to the maximum acceleration V max Constraint of conditions, the maximum jerk J cannot be reached in the processing of the section max So the time T of the maximum jerk acceleration period is maintained 2 =0. At the same time, from A max ≥A 1 It is obtained that the motion of the section does not reach the maximum acceleration A max (T 4 =0). According to maximum speed V max Deriving the maximum jerk J which can be reached 2 ：
Time T of acceleration period of increased jerk 1 Following the maximum jerk change:
because S is greater than or equal to S 1 The length of the processing line segment meets the maximum speed V max The conditions of the section are obtained to reach V max Displacement S at the time 7 ：
S 7 ＝2×4J 2 ·T 1 3 (39)
Therefore, the constant speed period time T 8 The method comprises the following steps:
(2.4) if A max ＜A 1 ，V max ＜V 1 ，S≥S 1 Or S < S 1
At this time, the processing length S or the maximum acceleration A is explained max Conditions and maximum speed V max Constraint of conditions, the maximum jerk J cannot be reached in the processing of the section max (T 2 =0). Solving the maximum jerk J which can be achieved according to the machining length S 3 Corresponding maximum acceleration a 5 And at bestHigh speed V 6 ：
A 6 ＝J 3 ·T 1 (43)
V 6 ＝2J 3 ·T 1 2 (44)
(2.4.1) if A 6 ＜A max ,V 6 ＜V max
At this time, it is explained that the processing in this section is performed at a maximum jerk of J 3 In the case of (a), the maximum acceleration A is not reached max And maximum speed V max So the acceleration period time T of the maximum acceleration is maintained 4 At uniform speed time T 8 Are all 0. The processing of the section only has an acceleration section with increased jerk, and the time is as follows:
(2.4.2) if A 6 ≥A max ,V 6 ＜V max
At this time, it is explained that due to the maximum acceleration A max Constraint of conditions, jerk J cannot be reached in the present stage of processing 3 And cannot reach maximum speed V max (T 8 =0). According to A max To determine the maximum jerk J that can be reached 4 ：
The acceleration period time T for maintaining the maximum acceleration can be obtained by solving the equation 4 ：
/>
(2.4.3) if A 6 ＜A max ,V 6 ≥V max
At this time, it is explained that due to the maximum speed V max Constraint of conditions, jerk J cannot be reached in the present stage of processing 3 And cannot reach maximum speed A max (T 4 =0). According to V max To determine the maximum jerk J that can be reached 5 ：
The time T of the constant speed section can be obtained by the processing length S 8 ：
Wherein S is 8 ＝2×(4J 5 ·T 1 3 )。
(2.4.4) if A 6 ≥A max ,V 6 ≥V max
At this time, it is explained that due to the maximum acceleration A max Conditions and maximum speed V max Constraint of conditions, the maximum jerk achieved by this section of energy addition is less than J 3 Because A max And V max All have a constraint on the maximum jerk, so that they are respectively based on the maximum acceleration A max And maximum speed V max Solving the maximum jerk J which can be achieved 6 ,J 7 。
(2.4.4. A) if J 6 ≥J 7
At this time, it is explained that the maximum acceleration A can be reached in the present stage of processing max But due to the maximum acceleration A max Constraint of conditions that the present segment of processing is unable to reach maximum speed V max And maximum jerk J max . The specific planning method can refer to the step (2.4.2).
(2.4.4.b)J 6 ＜J 7
At this time, it is explained that the maximum acceleration V can be reached in the present stage of processing max But due to maximum speed V max Constraint of conditions that the processing of the present section cannot reach the maximum acceleration A max And maximum jerk J max . The specific planning method can refer to the step (2.4.3).
To this end, according to the maximum jerk J max Condition, maximum acceleration A max Condition, maximum speed V max And under the condition, the time of each stage in the whole processing process is obtained, and the speed planning of the processing is completed.
The workflow and working principle of the present invention will be further described with a preferred embodiment of the present invention.
Case 1. The motion parameters and the processing information of the triaxial numerically controlled milling machine are shown in table 3.
TABLE 3 Table 3
| Initial parameters | Jounce | J max | A max | V max | S |
| Parameter value | 10 7 mm/s 4 | 5×10 4 mm/s 3 | 1500mm/s 2 | 100mm/s | 20mm |
The acceleration and deceleration control method model and the motion speed planning algorithm can be utilized to output a speed curve, an acceleration curve and a jerk curve through Matlab by utilizing C language programming in the visual studio 2013.
First, according to the machining parameters and the motion parameters of the machine tool, the time of each stage can be calculated:
T 1 ＝T 3 ＝T 5 ＝T 7 ＝T 9 ＝T 11 ＝T 13 ＝T 15 ＝0.005236s
T 2 ＝T 6 ＝T 10 ＝T 14 ＝0.024764s
T 4 ＝T 12 ＝0.031431s
T 8 ＝0.098097s
then according to the acceleration and deceleration algorithm model formulas (1) - (4), the displacement, the speed and the acceleration in the processing process are solved, and a specific acceleration and deceleration curve is shown in fig. 6.
Case 2. The motion parameters and the processing information of the triaxial numerically controlled milling machine are shown in table 4.
TABLE 4 Table 4
| Initial parameters | Jounce | J max | A max | V max | S |
| Parameter value | 10 7 mm/s 4 | 5×10 4 mm/s 3 | 1500mm/s 2 | 100mm/s | 10mm |
First, according to the machining parameters and the motion parameters of the machine tool, the time of each stage can be calculated:
T 1 ＝T 3 ＝T 5 ＝T 7 ＝T 9 ＝T 11 ＝T 13 ＝T 15 ＝0.005236s
T 2 ＝T 6 ＝T 10 ＝T 14 ＝0.024764s
T 4 ＝T 12 ＝0.030675s
T 8 ＝0s
then according to the acceleration and deceleration algorithm model formulas (1) - (4), the displacement, the speed and the acceleration in the processing process are solved, and a specific acceleration and deceleration curve is shown in fig. 7.
And 3. According to the motion parameters and the processing information of the three-axis numerical control milling machine of the case 1, making a speed plan of S-shaped acceleration and deceleration, 7-section trigonometric function acceleration and deceleration and continuous acceleration and deceleration based on time-optimal acceleration and deceleration, obtaining the processing information as shown in the following table 5, and outputting a motion curve as shown in fig. 8.
TABLE 5
| Acceleration and deceleration control method | Length of processing mm | Processing time ms | Maximum jerk fluctuation mm/s 4 |
| S-shaped acceleration and deceleration method | 20 | 296.7 | 5×10 7 |
| Trigonometric function acceleration and deceleration method | 20 | 304.6 | 3.3×10 5 |
| The invention relates to an acceleration and deceleration method | 20 | 331.8 | 9×10 5 |
As can be seen from the table, compared with the acceleration and deceleration of the trigonometric function, the acceleration and deceleration method provided by the invention improves the processing efficiency by about 8.9% under the condition that the fluctuation of the acceleration and deceleration is not great; compared with the S-shaped acceleration and deceleration, under the condition that the processing efficiency is not greatly different, the fluctuation of the maximum jerk is reduced by about two orders of magnitude, and the jerk curve of the acceleration and deceleration method of the invention is obviously smoother than that of the S-shaped acceleration and deceleration as shown in the comparison graph of the motion curve of the prior art S-shaped acceleration and deceleration, the prior art trigonometric function acceleration and deceleration and the acceleration and deceleration processing of the invention provided by the embodiment of the invention in fig. 5 and the figure 8.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any adaptations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
It is to be understood that the present disclosure is not limited to the precise arrangements and instrumentalities shown in the drawings, and that various modifications and changes may be effected without departing from the scope thereof. The scope of the present disclosure should be limited by the attached claims.
Claims (9)
1. The acceleration and deceleration control method based on the time optimal jerk continuous is characterized by comprising the following steps of:
the numerical control system carries out multistage division of the machining process according to the machining motion condition, and analyzes the conditions of the maximum jerk, the maximum acceleration and the maximum speed in the whole machining process;
analyzing whether each stage of the processing process exists according to the motion condition of the processing to obtain the running time of each stage of the processing process, and further obtaining a motion curve after the processing speed planning;
dividing the whole processing time into 15 sections, respectively 0-t 1 ，t 1 ～t 2 ，t 2 ～t 3 ，…，t 14 ～t 15 Defining the time interval of each time period as T i T is then i The corresponding time period is t i-1 ～t i The method comprises the steps of carrying out a first treatment on the surface of the Wherein i=1, 2, 15,0 to t 7 To accelerate the phase, t 7 ～t 8 At a constant speed, t 8 ～t 15 For the deceleration phase, T 1 For accelerating movement with increased jerk, T 2 For maximum jerk acceleration movement, T 3 For acceleration movement with reduced jerk, T 4 To maintain maximum acceleration of the acceleration movement, T 5 For acceleration movement with reduced jerk, T 6 Acceleration movement with minimum jerk, T 7 For accelerating movement with increased jerk, T 8 For uniform movement, T 9 ～T 15 For decelerating movement, and accelerating process T 1 ～T 7 Symmetrical;
in the analysis of the maximum jerk during processing, sin 2 (x) Calculating as a basis function to obtain an expression j (t) of jerk:
wherein J is max Is the maximum jerk during operation;
maximum jerk Jounce, maximum jerk J according to the length S of the machining track max Maximum acceleration A max Maximum speed V max And the motion parameters are used for planning a displacement curve, a speed curve, an acceleration curve and a jerk curve of the whole processing process in real time.
2. The time-optimal jerk-based continuous acceleration and deceleration control method of claim 1, wherein the real-time planning of the displacement curve, the velocity curve, the acceleration curve, and the jerk curve of the entire machining process specifically comprises:
(1.1) dividing the whole numerical control machining process into 15 sections, maximum jerk J of acceleration section and deceleration section max And maximum acceleration A max Identical, T 1 Time of acceleration period, T, indicating increase in jerk 2 Indicating the acceleration period time for maintaining maximum jerk, T 4 The acceleration period time representing the maximum acceleration is maintained:
T 1 ＝T 3 ＝T 5 ＝T 7 ＝T 9 ＝T 11 ＝T 13 ＝T 15
T 2 ＝T 6 ＝T 10 ＝T 14
T 4 ＝T 12
first, it is determined whether the maximum jerk J can be reached max To reach J max Acceleration A of (2) 1 Velocity V 1 And displacement S 1 The conditions are as follows:
(2.1) if A max ≥A 1 ，V max ≥V 1 ，S≥S 1 The processing of the section can reach the maximum jerk J max Time T of acceleration period of increased jerk 1 The method comprises the following steps:
then, it is also necessary to determine whether the maximum acceleration A can be reached max To reach A max Velocity V of (2) 2 And displacement S 2 The conditions are as follows:
V 2 ＝2J max T 1 2 +3J max T 1 T 2 +J max T 2 2
S 2 ＝2×(4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 )
(2.2) if A max ＜A 1 ，V max ≥V 1 ，S≥S 1 Due to maximum acceleration A max Constraint of conditions, the maximum jerk J cannot be reached in the processing of the section max Time T for maintaining maximum jerk acceleration period 2 =0; according to maximum acceleration A max Find the maximum jerk J that can be reached 1 ：
Time T of acceleration period of increased jerk 1 Following the maximum jerk change:
then, it is determined that the maximum speed V can be reached max According to V max The determined displacement condition S 6 ：
(2.3) if A max ≥A 1 ，V max ＜V 1 ，S≥S 1 Due to maximum acceleration V max Constraint of conditions, the maximum jerk J cannot be reached in the processing of the section max Time T for maintaining maximum jerk acceleration period 2 =0; at the same time, from A max ≥A 1 It is obtained that the motion of the section does not reach the maximum acceleration A max ，T 4 =0; according to maximum speed V max Deriving the maximum jerk J which can be reached 2 ：
Time T of acceleration period of increased jerk 1 Following the maximum jerk change:
because S is greater than or equal to S 1 The length of the processing line segment meets the maximum speed V max The conditions of the section are obtained to reach V max Displacement S at the time 7 ：
S 7 ＝2×4J 2 ·T 1 3
Therefore, the constant speed period time T 8 The method comprises the following steps:
(2.4) if A max ＜A 1 ，V max ＜V 1 ，S≥S 1 Or S < S 1 ，
Due to the working length S or the maximum acceleration A max Conditions and maximum speed V max Constraint of conditions, the maximum jerk J cannot be reached in the processing of the section max ，T 2 =0; solving the maximum jerk J which can be achieved according to the machining length S 3 Corresponding maximum acceleration a 5 And maximum speed V 6 ：
A 6 ＝J 3 ·T 1
V 6 ＝2J 3 ·T 1 2 。
3. The time-optimal jerk-based continuous acceleration/deceleration control method of claim 2, wherein the step (2.1) further comprises:
(2.1.1) if V max ≥V 2 ,S≥S 2 ，
The processing can reach and maximize the acceleration A max And maintains the time T of the maximum jerk acceleration period 2 The method comprises the following steps:
wherein,
the receiver judges whether the maximum speed V can be reached max To reach V max Is of the displacement S of (2) 3 The conditions are as follows:
(2.1.2) if V max ＜V 2 ,S≥S 2 The processing of this section is due to the maximum speed V max Constraint of conditions, failure to reach maximum acceleration A max The method comprises the steps of carrying out a first treatment on the surface of the According to V max ＝2J max T 1 2 +3J max T 1 T 2 +J max T 2 2 Solving the acceleration period time T of keeping the maximum jerk 2 ；
Time T of constant velocity section 8 Expressed as:
wherein S is 4 ＝2×(4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 )；
(2.1.3) if S < S 2 Since the working length S is too short, the maximum acceleration A cannot be reached max The method comprises the steps of carrying out a first treatment on the surface of the Deriving the maximum acceleration A achievable from the working length S 3 Judging the maximum speed V currently reached 4 Whether or not the maximum speed V can be satisfied max Conditions;
according to s=2× (4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 ) Solving the acceleration period time T for keeping the maximum jerk 2 ；
Solving for the maximum acceleration A according to the working length S 3 And maximum speed V 4 Conditions are as follows:
A 3 ＝J max ·T 1 +J max ·T 2
V 4 ＝2J max T 1 2 +3J max T 1 T 2 +J max T 2 2 。
4. the time-optimal jerk-based continuous acceleration/deceleration control method of claim 3, wherein the step (2.1.1) further comprises:
(2.1.1. A) if S.gtoreq.S 3 The processing of the section can reach the maximum speed V max Acceleration period time T for maintaining maximum acceleration 4 The method comprises the following steps:
according to the displacement S and the maximum velocity V max For time T of constant velocity section 8 And (3) carrying out solving:
(2.1.1. B) if S < S 3 Because the processing length S of the section is too short, the maximum speed V cannot be reached max Without constant velocity stage T 8 =0; according to the displacement formula, a formula is deducedSolving the acceleration period time T for obtaining the maximum acceleration 4 ；
Maximum speed V achievable at this time 3 Is that
V 3 ＝V 2 +T 4 ·A max ；
The step (2.1.3) further comprises:
(2.1.3. A) if V 4 ≥V max The processing of the section can reach the maximum speed V max But cannot reach the maximum acceleration A max The method comprises the steps of carrying out a first treatment on the surface of the According to V max ＝2J max T 1 2 +3J max T 1 T 2 +J max T 2 2 Solving the acceleration period time T of keeping the maximum jerk 2 ：
Solving the time T of the constant speed section according to the displacement S 8 ：
Wherein S is 5 ＝2×(4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 )；
(2.1.3. B) if V 4 ＜V max The processing of the section can not reach the maximum acceleration A max And maximum speed V max Acceleration period time T for maintaining maximum acceleration 4 And time T of constant velocity section 8 Is 0; according to solving equation s=2× (4J max T 1 3 +8J max T 1 2 T 2 +5J max T 1 T 2 2 +J max T 2 3 ) Deriving the acceleration period time T for maintaining maximum jerk 2 。
5. The time-optimal jerk-based continuous acceleration/deceleration control method of claim 2, wherein the step (2.2) further comprises:
(2.2.1) if S > S 6 The working length S is sufficient to achieve a maximum speed V max Obtaining the acceleration period time T for maintaining the maximum acceleration 4 And a constant velocity period of timeT 8 ：
(2.2.2) if S is less than or equal to S 6 In the present stage of processing, the maximum speed V cannot be reached due to the too short processing length S max ，T 8 =0; by solving equationsThe acceleration period time T for maintaining the maximum acceleration 4 。
6. The time-optimal jerk-based continuous acceleration/deceleration control method of claim 2, wherein said step (2.4)
(2.4.1) if A 6 ＜A max ,V 6 ＜V max The processing of the section is that the maximum jerk is J 3 In the case of (a), the maximum acceleration A is not reached max And maximum speed V max Acceleration period time T for maintaining maximum acceleration 4 At uniform speed time T 8 Are all 0; the processing of the section only has an acceleration section with increased jerk, and the time is as follows:
(2.4.2) if A 6 ≥A max ,V 6 ＜V max Due to maximum acceleration A max Constraint of conditions, jerk J cannot be reached in the present stage of processing 3 And cannot reach maximum speed V max ，T 8 =0; according to A max Determining the maximum jerk J that can be achieved 4 ：
By solving equationsThe acceleration period time T for maintaining the maximum acceleration 4 ；
(2.4.3) if A 6 ＜A max ,V 6 ≥V max Due to maximum speed V max Constraint of conditions, jerk J cannot be reached in the present stage of processing 3 And cannot reach maximum speed A max ，T 4 =0; according to V max Determining the maximum jerk J that can be achieved 5 ：
Obtaining the time T of the constant speed section through the processing length S 8 ：
Wherein S is 8 ＝2×(4J 5 ·T 1 3 )；
(2.4.4) if A 6 ≥A max ,V 6 ≥V max Due to maximum acceleration A max Conditions and maximum speed V max Constraint of condition, the most reached by this section of additionThe large jerk is smaller than J 3 Because A max And V max All have constraint on the maximum jerk, respectively according to the maximum acceleration A max And maximum speed V max Solving the maximum jerk J which can be achieved 6 ,J 7 ；
(2.4.4. A) if J 6 ≥J 7 The maximum acceleration A can be reached in the processing of the section max But due to the maximum acceleration A max Constraint of conditions that the present segment of processing is unable to reach maximum speed V max And maximum jerk J max ；
(2.4.4.b)J 6 ＜J 7 The maximum acceleration V can be achieved in the processing of the section max Due to maximum speed V max Constraint of conditions that the processing of the present section cannot reach the maximum acceleration A max And maximum jerk J max 。
7. A numerical control system for implementing the time-optimal jerk-based continuous acceleration-deceleration control method of any one of claims 1 to 6, characterized in that the numerical control system includes:
the maximum jerk analysis module is used for analyzing the maximum jerk of a plurality of stages of processing process division according to the motion condition of numerical control processing;
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages of processing process division according to the motion condition of numerical control processing;
the maximum speed analysis module is used for analyzing the maximum speeds of a plurality of stages of machining process division according to the movement conditions of numerical control machining;
and the processing speed motion curve acquisition module is used for analyzing whether each stage of the processing process exists according to the processing conditions so as to obtain the running time of each stage of the processing process and further obtain the motion curve after the processing speed planning.
8. A storage medium storing a program for receiving a user input, the stored computer program causing an electronic device to execute the time-optimal jerk-based continuous acceleration/deceleration control method of any one of claims 1 to 6.
9. A numerical control machine tool, wherein the numerical control machine tool implements the continuous acceleration/deceleration control method according to any one of claims 1 to 6 based on time-optimal jerk.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111305713.5A CN114035504B (en) | 2021-11-05 | 2021-11-05 | Acceleration and deceleration control method based on time optimization, numerical control system, medium and machine tool |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111305713.5A CN114035504B (en) | 2021-11-05 | 2021-11-05 | Acceleration and deceleration control method based on time optimization, numerical control system, medium and machine tool |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114035504A CN114035504A (en) | 2022-02-11 |
| CN114035504B true CN114035504B (en) | 2024-03-19 |
Family
ID=80142938
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111305713.5A Active CN114035504B (en) | 2021-11-05 | 2021-11-05 | Acceleration and deceleration control method based on time optimization, numerical control system, medium and machine tool |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114035504B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20140094313A (en) * | 2013-01-22 | 2014-07-30 | 한국항공우주연구원 | Friction compensator and compensating method using thereof |
| WO2017113069A1 (en) * | 2015-12-28 | 2017-07-06 | 深圳配天智能技术研究院有限公司 | S-shaped curve planning method and device, and numerically-controlled machine tool |
| CN108287527A (en) * | 2017-07-18 | 2018-07-17 | 山东大学 | A kind of improvement S curve Acceleration-deceleration Control Method based on trigonometric function |
| CN110865610A (en) * | 2019-10-18 | 2020-03-06 | 中国工程物理研究院机械制造工艺研究所 | Tool path interpolation and speed planning method based on machine tool vibration suppression |
| CN112975986A (en) * | 2021-03-25 | 2021-06-18 | 珞石（北京）科技有限公司 | Mechanical arm point-to-point trajectory planning method and device based on radial basis function |
-
2021
- 2021-11-05 CN CN202111305713.5A patent/CN114035504B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20140094313A (en) * | 2013-01-22 | 2014-07-30 | 한국항공우주연구원 | Friction compensator and compensating method using thereof |
| WO2017113069A1 (en) * | 2015-12-28 | 2017-07-06 | 深圳配天智能技术研究院有限公司 | S-shaped curve planning method and device, and numerically-controlled machine tool |
| CN108287527A (en) * | 2017-07-18 | 2018-07-17 | 山东大学 | A kind of improvement S curve Acceleration-deceleration Control Method based on trigonometric function |
| CN110865610A (en) * | 2019-10-18 | 2020-03-06 | 中国工程物理研究院机械制造工艺研究所 | Tool path interpolation and speed planning method based on machine tool vibration suppression |
| CN112975986A (en) * | 2021-03-25 | 2021-06-18 | 珞石（北京）科技有限公司 | Mechanical arm point-to-point trajectory planning method and device based on radial basis function |
Non-Patent Citations (4)
| Title |
|---|
| PCB钻孔机数控系统的加减速控制方法研究;郭钊;游有鹏;张礼兵;杨雪峰;;伺服控制;20111230(08);全文 * |
| S-CURVE ALGORITHM OF ACCELERATION/DECELERATION WITH SMOOTHLY-LIMITED JERK IN HIGH-SPEED EQUIPMENT CONTROL TASKS;V. Kombarov;《SCIENCE JOURNAL》;20191130;全文 * |
| 多项式加减速控制方法研究;徐川;王永章;刘源;;组合机床与自动化加工技术;20090920(09);全文 * |
| 数控加工小线段高速平滑衔接插补算法;李小清;朱凯;;组合机床与自动化加工技术;20100920(09);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114035504A (en) | 2022-02-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107850887B (en) | S-shaped curve planning method and device and numerical control machine tool | |
| Dong et al. | Smooth feedrate planning for continuous short line tool path with contour error constraint | |
| Pateloup et al. | Bspline approximation of circle arc and straight line for pocket machining | |
| CN102540978B (en) | High-speed processing-oriented surface quality preferred spline real-time interpolation method | |
| CN102147600B (en) | Numerical control interpolation system for real-time generation of curvature-continuous path | |
| CN103801981B (en) | A kind of quartic polynomial velocity planning algorithm for spline interpolation | |
| CN102945020B (en) | Speed forecasting method, as well as numerical control device and numerical control system thereof | |
| CN103592891A (en) | Method for cutter-axis vector fairing of complex curved surface five-axis numerical control machining based on kinematical constraints | |
| CN111158318B (en) | Flexible acceleration and deceleration planning method for asymmetric quartic curve | |
| CN107765648A (en) | A kind of feed speed method and device for planning of CNC processing | |
| CN109426151A (en) | Real-time flexible acceleration/deceleration control algorithm based on adaptive prediction and prediction correction | |
| Ni et al. | A bidirectional adaptive feedrate scheduling method of NURBS interpolation based on S-shaped ACC/DEC algorithm | |
| CN104281099A (en) | NURBS direct interpolation method and device with processing characteristics considered | |
| CN109901518B (en) | Method for planning acceleration and deceleration speed of numerical control machine tool under constant force constraint condition | |
| CN112486101B (en) | NURBS curve self-adaptive look-ahead interpolation method | |
| CN106647637A (en) | Trigonometric function acceleration and deceleration control method for high-quality machining | |
| CN107272598A (en) | Nurbs curve interpolating method known to a kind of machining path length | |
| CN107844058A (en) | A kind of curve movement Discrete Dynamic Programming method | |
| CN105629882A (en) | Trigonometric function speed planning method used for spline interpolation | |
| CN103163837B (en) | A kind of cutter path adaptive management system and method towards five-shaft numerical control processing | |
| CN114035504B (en) | Acceleration and deceleration control method based on time optimization, numerical control system, medium and machine tool | |
| Shi et al. | The look-ahead function-based interpolation algorithm for continuous micro-line trajectories | |
| JP2002222008A (en) | Numerically controlled curved surface processing device | |
| Li et al. | S-model speed planning of NURBS curve based on uniaxial performance limitation | |
| Luo et al. | Speed planning algorithm based on improved S-type acceleration and deceleration model |
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 |