CN114035504A - 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 PDF

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CN114035504A
CN114035504A CN202111305713.5A CN202111305713A CN114035504A CN 114035504 A CN114035504 A CN 114035504A CN 202111305713 A CN202111305713 A CN 202111305713A CN 114035504 A CN114035504 A CN 114035504A
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acceleration
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jerk
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CN114035504B (en
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王太勇
陈木正
刘杨帆
张永宾
邢洁济
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Tianjin University
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    • 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
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Abstract

The invention belongs to the technical field of numerical control in mechanical manufacturing engineering, and discloses an acceleration and deceleration control method based on time optimization, a numerical control system, a medium and a machine tool. Dividing the machining process of the numerical control system into a plurality of sections, and analyzing the conditions of maximum acceleration, maximum acceleration and maximum speed in the machining process according to the motion conditions of numerical control machining; and analyzing whether each stage of the machining process exists according to the machining conditions to obtain the running time of each stage of the machining process, and further obtaining the motion curve after the machining speed is planned. Compared with the existing trigonometric function acceleration and deceleration control method, the acceleration and acceleration curve can be smoothly and continuously realized, but compared with trigonometric function acceleration and deceleration, the method can keep the maximum acceleration for processing, can more effectively exert the motion performance of the numerical control machine and improve the processing efficiency.

Description

Acceleration and deceleration control method based on time optimization, numerical control system, medium and machine tool
Technical Field
The invention belongs to the technical field of numerical control in mechanical manufacturing engineering, and particularly relates to a time-optimal acceleration continuous acceleration and deceleration control method and system.
Background
At present, the manufacturing industry is an important support column of national economy, the machine manufacturing industry is the core of the manufacturing industry, numerical control machining has a non-negligible status in the machine manufacturing industry, and the numerical control machining has wide application in machining complex parts and the like. In recent years, the research on interpolation algorithms for numerical control machining by experts has been increasing year by year, and becomes a popular research on numerical control systems. The acceleration and deceleration control is used as an important component of numerical control interpolation machining, and has important significance for improving the numerical control machining precision and efficiency.
The earliest used T-type acceleration and deceleration can cause sudden change of acceleration at the beginning and end of machining, cause vibration in the machining process and affect the machining quality. At present, S-type acceleration and deceleration are mostly used, the machining efficiency is high, the acceleration is continuous, but the problem of sudden acceleration change exists in the machining process. The trigonometric acceleration/deceleration is superior to S-type acceleration/deceleration in the continuity of the acceleration during machining, but is slightly lower than the S-type acceleration/deceleration in the machining efficiency. In the conventional research, "a continuous acceleration and deceleration algorithm research of acceleration and deceleration [ J ]. machine manufacturing, 2021", the proposed sine function acceleration and deceleration can realize the continuous acceleration, but in the acceleration and deceleration planning process, the maximum acceleration only occurs in the peak point, and the maximum acceleration cannot be continuously used for acceleration or deceleration, so that the motion performance of the numerical control machine tool is not fully exerted, and the machining efficiency is low. Therefore, the trigonometric function accelerates and decelerates, the acceleration and deceleration curve is smooth, the smoothness of movement can be ensured, but the processing efficiency is low; s-type acceleration/deceleration has high processing efficiency, but cannot ensure smoothness of motion control.
Through the above analysis, the problems and defects of the prior art are as follows:
(1) in the prior art, in machining control, a numerical control system causes vibration and impact due to sudden change of acceleration or jerk, so that the machining quality is influenced.
(2) In the prior art, the numerical control machine tool cannot keep the maximum acceleration for processing, and the processing efficiency is low.
The difficulty in solving the above problems and defects is: the trigonometric function acceleration and deceleration adopted in numerical control machining can realize the continuity of the acceleration, but in the whole machining process, due to the characteristics of the trigonometric function, the maximum acceleration only exists on a peak point, the maximum acceleration cannot be fully utilized for acceleration, and the motion performance of the numerical control machine cannot be fully utilized. At present, the processing research for keeping the maximum acceleration in trigonometric function acceleration and deceleration is less, only S-type acceleration and deceleration can realize the processing for keeping the maximum acceleration, but the acceleration is discontinuous, and vibration and impact are caused in the processing. Therefore, in order to perform machining while maintaining the maximum jerk, it is necessary to analyze and compare the trigonometric acceleration and the S-shaped acceleration, and it is also necessary to control and analyze the jerk during machining, and to analyze conditions such as the maximum jerk, the maximum acceleration, and the maximum speed.
The significance 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, ensure the continuity of the acceleration and deceleration of the numerical control machining, enhance the acceleration and deceleration efficiency 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 disclosed embodiment of the invention provides a continuous acceleration and deceleration control method based on time optimal acceleration. In particular to a continuous acceleration and deceleration control method based on time optimal acceleration.
The technical scheme is as follows: a time-optimal acceleration continuous acceleration and deceleration control method is characterized in that a machining process of a numerical control system is divided into 15 sections, conditions of maximum acceleration, maximum acceleration and maximum speed in the machining process are analyzed according to motion conditions of numerical control machining, whether each section exists or not is discussed according to the machining conditions, so that running time of each section is obtained, and a motion curve after speed planning is further obtained.
Another object of the present invention is to provide a numerical control system for implementing the acceleration/deceleration control method for continuous acceleration/deceleration based on time optimization, the numerical control system including:
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages divided in the machining process according to the motion condition of numerical control machining;
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages divided in the machining process according to the motion conditions of the numerical control machining;
the maximum speed analysis module is used for analyzing the maximum speed of a plurality of stages divided in the machining process according to the motion 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 program storage medium for receiving a user input, the stored computer program causing an electronic device to execute the acceleration/deceleration control method for acceleration rate continuation based on time optimization.
Another object of the present invention is to provide a numerically controlled machine tool that implements the acceleration and deceleration control method based on time-optimized acceleration rate continuation.
By combining all the technical schemes, the invention has the advantages and positive effects that:
the acceleration and deceleration control method of the invention is compared with the S-shaped acceleration and deceleration method and the existing trigonometric function acceleration and deceleration control method of the prior art, the same track is processed under the same condition, and different acceleration and deceleration curves and processing parameter tables are obtained. As can be seen from table 2, compared with the trigonometric function acceleration and deceleration, the acceleration and deceleration method provided herein improves the processing efficiency by about 3.8% under the condition that the acceleration fluctuation is not much different; compared with S-type acceleration and deceleration, the fluctuation of the maximum acceleration is reduced by about two orders of magnitude under the condition that the processing efficiency is not greatly different.
TABLE 1 processing parameter Table
Initial parameters Jounce Jmax Amax Vmax
Parameter value 107mm/s4 5×104mm/s3 1500mm/s2 100mm/s
TABLE 2 comparison table for acceleration and deceleration processing
Acceleration and deceleration control method Length of processing mm Machining time ms Maximum acceleration fluctuation mm/s4
S-type acceleration and deceleration method 86 1422.6 5×107
Trigonometric function acceleration and deceleration square 86 1553.3 3.3×105
The invention relates to an addition deceleration method 86 1493.0 9×105
Compared with the existing S-shaped acceleration and deceleration control method, the acceleration curve and the jerk curve are smoother under the condition that the machining efficiency is not large as shown in figure 5, so that the vibration and impact caused by acceleration or jerk in a numerical control system are reduced, and the machining quality is improved. Compared with the existing trigonometric function acceleration and deceleration control method, the method and the device realize smooth and continuous acceleration and acceleration curves, but compared with trigonometric function acceleration and deceleration, the method and the device can keep the maximum acceleration for processing, can more effectively exert the motion performance of the numerical control machine and improve 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.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure.
Fig. 1 is a flowchart of a time-based optimal acceleration-continuous acceleration/deceleration control method according to an embodiment of the present invention.
Fig. 2 is a 7-segment S-shaped acceleration/deceleration model curve in the prior art according to an embodiment of the present invention.
In fig. 2: t isiIs represented by stages ti-1～tiTime of (i ═ 1,2,. cndot., 7), VmaxFor maximum speed during operation, AmaxFor maximum acceleration during operation, JmaxFor maximum jerk during operation
Fig. 3 is a trigonometric function type acceleration/deceleration model curve in the prior art provided by an embodiment of the present invention.
In fig. 3: t isiIs represented by stages ti-1～tiTime of (i ═ 1,2,. cndot., 7), VmaxFor maximum speed during operation, AmaxFor maximum acceleration during operation, JmaxIs the maximum jerk during operation.
Fig. 4 is a time-optimal acceleration-continuous acceleration/deceleration control model curve provided by the present invention according to an embodiment of the present invention.
In fig. 4: t isiIs represented by stages ti-1～tiTime of (i ═ 1,2,. cndot., 15), VmaxFor maximum speed during operation, AmaxFor maximum acceleration during operation, JmaxIs the maximum jerk during operation.
Fig. 5 is a first comparison diagram of the motion curves of S-type acceleration and deceleration, trigonometric function acceleration and deceleration, and acceleration and deceleration processing according to the present invention.
Fig. 6 is a graph of acceleration and deceleration movement according to the actual processing of case 1 according to the embodiment of the present invention.
Fig. 7 is a graph of acceleration and motion actually processed according to case 2, provided by an embodiment of the present invention.
Fig. 8 is a motion curve diagram ii output by case 3 according to the motion parameters and the processing information of the three-axis numerically controlled milling machine of case 1, and performing S-type acceleration/deceleration, 7-segment trigonometric function acceleration/deceleration, and the speed planning of the present invention based on the time-optimal acceleration continuous acceleration/deceleration.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather should be construed as broadly as the present invention is capable of modification in various respects, all without departing from the spirit and scope of the present invention.
As shown in fig. 1, the acceleration and deceleration control method based on time-optimal continuous jerk according to the embodiment of the present invention includes:
s101, dividing the machining process of the numerical control system into a plurality of sections;
s102, analyzing the conditions of maximum acceleration, maximum acceleration and maximum speed in the machining process according to the motion conditions of numerical control machining;
and S103, analyzing whether each stage of the machining process exists or not according to the machining conditions to obtain the running time of each stage of the machining process, and further obtaining the motion curve after the machining speed is planned.
The invention also provides a numerical control system for implementing the acceleration and deceleration control method based on time optimal acceleration continuous acceleration, which comprises the following steps:
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages divided in the machining process according to the motion condition of numerical control machining;
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages divided in the machining process according to the motion conditions of the numerical control machining;
the maximum speed analysis module is used for analyzing the maximum speed of a plurality of stages divided in the machining process according to the motion 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 solution of the present invention is further described below with reference to specific examples.
Examples
As shown in fig. 2, a 7-segment S-shaped acceleration/deceleration model curve in the prior art. In fig. 2: t isiIs represented by stages ti-1～tiTime of (i ═ 1,2,. cndot., 7), VmaxFor maximum speed during operation, AmaxFor maximum acceleration during operation, JmaxIs the maximum jerk during operation.
Fig. 3 is a curve of a prior art acceleration/deceleration model of sine trigonometric function type. In fig. 3: t isiIs represented by stages ti-1～tiTime of (i ═ 1,2,. cndot., 7), VmaxFor maximum speed during operation, AmaxFor maximum acceleration during operation, JmaxIs the maximum jerk during operation.
As shown in fig. 4, the acceleration and deceleration control method based on time-optimized continuous jerk provided by the present invention includes: setting the whole motion time of numerical control machining as T, the invention divides the whole machining time into 15 sections which are respectively 0-T1，t1～t2，t2～t3，…，t14～t15Defining a time interval of T for each time segmenti(i ═ 1,2,. cndot., 15), then TiCorresponding to a time period of ti-1～ti(i ═ 1,2,. cndot., 15). Wherein, 0 to t7For the acceleration phase, t7～t8At a constant speed stage, t8～t15For the deceleration phase, T1For accelerated motion with increased jerk, T2Acceleration movement for maximum jerk, T3For accelerated motion with reduced jerk, T4To maintain the acceleration movement at maximum acceleration, T5For accelerated motion with reduced jerk, T6Acceleration movement for minimum jerk, T7For accelerated motion with increased jerk, T8For uniform motion, T9～T15For decelerating movement, with an acceleration process T1～T7And (4) symmetry. Therefore, the acceleration and deceleration algorithm is described by taking an acceleration stage and a constant speed stage as examples.
In order to ensure the continuity of the acceleration, the invention uses sin2(x) The expression j (t) related to the acceleration in the acceleration and deceleration control method is obtained by calculating as a basis function:
Figure BDA0003340167440000071
wherein, JmaxIs the maximum jerk during operation.
In a preferred embodiment of the present invention, j (t) can be integrated to obtain an expression a (t) of acceleration:
Figure BDA0003340167440000072
wherein, JmaxFor maximum jerk during operation, ai(i ═ 2,3,. cndot., 6) is at time t ═ tiThe instantaneous acceleration of (a) can be expressed as:
Figure BDA0003340167440000081
a2＝a1+Jmax·T2
Figure BDA0003340167440000082
a4＝a3
Figure BDA0003340167440000083
a6＝a5-Jmax·T6
Figure BDA0003340167440000084
in a preferred embodiment of the invention, the velocity expression v (t) may be integrated from the accelerometer expression a (t):
Figure BDA0003340167440000085
wherein, JmaxFor maximum jerk during operation, vsIs the initial processing speed, vi(i ═ 2,3, ·, 6) at time t ═ tiIs expressed as:
Figure BDA0003340167440000091
Figure BDA0003340167440000092
Figure BDA0003340167440000093
v4＝v3+a3·T4
Figure BDA0003340167440000094
Figure BDA0003340167440000095
Figure BDA0003340167440000096
in a preferred embodiment of the present invention, velocity expression v (t) may be integrated to obtain displacement expression s (t):
Figure BDA0003340167440000097
wherein, JmaxFor maximum jerk during operation, vsAs initial processing speed, si(i ═ 2,3,. 6) at time t ═ tiIs expressed as:
Figure BDA0003340167440000101
Figure BDA0003340167440000102
Figure BDA0003340167440000103
Figure BDA0003340167440000104
Figure BDA0003340167440000105
Figure BDA0003340167440000106
Figure BDA0003340167440000107
s8＝s7+v7·T8
in a preferred embodiment of the present invention, the present invention can be applied to the maximum jerk of the length S of the machining trajectoryAcceleration JmaxMaximum acceleration AmaxMaximum velocity VmaxAnd (5) the motion parameters are equal, and a displacement curve, a speed curve, an acceleration curve and an acceleration curve of the whole machining process are planned in real time.
(1.1) in the whole process, the invention divides the whole process into 15 sections, and because the parameter settings are the same, the invention has the maximum acceleration J of the acceleration section and the deceleration sectionmaxAnd maximum acceleration AmaxSame, so the speed accelerates from 0 to the maximum speed VmaxIs theoretically the sum speed from the maximum speed VmaxThe time to decelerate to 0 is the same, so the acceleration and deceleration sections are symmetric on the velocity curve, so in the subsequent derivation, T1Acceleration period time, T, representing an increase in jerk2Representing the time of the acceleration period, T, during which the maximum jerk is maintained4Represents the acceleration period time during which the maximum acceleration is maintained:
T1＝T3＝T5＝T7＝T9＝T11＝T13＝T15 (5)
T2＝T6＝T10＝T14 (6)
T4＝T12 (7)
first, the present invention determines whether the maximum jerk J can be reachedmaxTo give an arrival at JmaxAcceleration A of1Velocity V1And a displacement S1The conditions are as follows:
Figure BDA0003340167440000111
Figure BDA0003340167440000112
Figure BDA0003340167440000113
Figure BDA0003340167440000114
(2.1) if Amax≥A1，Vmax≥V1，S≥S1
It is shown that the maximum jerk J can be achieved in this stage of machiningmaxAt this time, the acceleration period of the jerk is increased1Comprises the following steps:
Figure BDA0003340167440000115
next, the present invention also needs to determine whether the maximum acceleration A can be reachedmaxTo obtain a result of reaching AmaxVelocity V of2And a displacement S2The conditions are as follows:
Figure BDA0003340167440000116
V2＝2JmaxT1 2+3JmaxT1T2+JmaxT2 2 (14)
S2＝2×(4JmaxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3) (15)
(2.1.1) if Vmax≥V2,S≥S2
It is now shown that the machining in this stage is able to reach a maximum acceleration AmaxAnd maintaining the time T of the maximum jerk acceleration period2It is also determined that:
Figure BDA0003340167440000117
wherein A is1Are the parameters in the formula (I) and,
Figure BDA0003340167440000118
next, it is necessary to judge whether or not the maximum speed V can be reachedmaxTo obtain a value of VmaxIs a displacement S3The conditions are as follows:
Figure BDA0003340167440000119
Figure BDA0003340167440000121
(2.1.1.a) if S.gtoreq.S3
It is now shown that the maximum speed V can be reached in this stage of the processmaxMaintaining the acceleration period T of maximum acceleration4The determination is as follows:
Figure BDA0003340167440000122
according to the displacement S and the maximum speed VmaxFor the time T of the uniform velocity section8And (3) solving:
Figure BDA0003340167440000123
(2.1.1.b) if S < S3
At this time, since the working length S is too short, the maximum speed V cannot be reachedmaxNo uniform velocity phase (T) is indicated80). The formula can be derived according to the displacement formula, and the acceleration period time T keeping the maximum acceleration is obtained by solving the formula4.
Figure BDA0003340167440000124
The maximum speed V that can be reached at this time3Is composed of
V3＝V2+T4·Amax (22)
(2.1.2) if Vmax＜V2,S≥S2
At this time, the maximum speed V is obtained in this stage of the processmaxConstraint of condition that maximum acceleration A cannot be reachedmax. So that the acceleration period time T for keeping the maximum acceleration can be solved according to the formula2：
Vmax＝2JmaxT1 2+3JmaxT1T2+JmaxT2 2 (23)
Time T of uniform velocity segment8Expressed as:
Figure BDA0003340167440000125
wherein S is4＝2×(4JmaxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3)。
(2.1.3) if S < S2
At this time, it is explained that the maximum acceleration A cannot be reached because the machining length S is too shortmax. The maximum acceleration A that can be achieved is obtained from the machining length S3Judging the currently reached maximum speed V4Whether or not the maximum speed V can be satisfiedmaxAnd (4) conditions.
According to the formula, the acceleration period time T for keeping the maximum acceleration is solved2
S＝2×(4JmaxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3) (25)
Solving the maximum acceleration A according to the machining length S3And a maximum speed V4Conditions are as follows:
A3＝Jmax·T1+Jmax·T2 (26)
V4＝2JmaxT1 2+3JmaxT1T2+JmaxT2 2 (27)
(2.1.3.a) if V4≥Vmax
It is now shown that the maximum speed V can be reached in this stage of the processmaxCannot achieve the maximum acceleration Amax. Therefore, the acceleration period time T for keeping the maximum acceleration can be solved according to the formula2：
Vmax＝2JmaxT1 2+3JmaxT1T2+JmaxT2 2 (28)
Then, the time T of the uniform speed section is solved according to the displacement S8：
Figure BDA0003340167440000131
Wherein S is5＝2×(4JmaxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3)。
(2.1.3.b) if V4＜Vmax
At this time, it is shown that the maximum acceleration A cannot be reached in this stage of processingmaxAnd a maximum speed VmaxSo that the acceleration period T of the maximum acceleration is maintained4And time T of uniform velocity segment8Is 0. Obtaining the acceleration period time T for keeping the maximum acceleration according to the solution equation2：
S＝2×(4JmaxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3) (30)
(2.2) if Amax＜A1，Vmax≥V1，S≥S1
This time illustrates the maximum acceleration AmaxConstrained by conditions, the maximum acceleration J cannot be reached in the processing of the sectionmaxSo that the time T of the maximum jerk acceleration period is maintained20. According to the maximum acceleration AmaxDetermining the maximum attainable jerk J1：
Figure BDA0003340167440000141
Time T of acceleration segment of jerk increase1Following maximum jerk change:
Figure BDA0003340167440000142
in a preferred embodiment of the present invention, the present invention determines that the maximum speed V can be reachedmaxAccording to VmaxThe obtained displacement condition S6：
Figure BDA0003340167440000143
(2.2.1) if S > S6
In this case, the machining length S is sufficient to reach the maximum speed VmaxTo obtain the acceleration period T for keeping the maximum acceleration4And a constant speed period T8：
Figure BDA0003340167440000144
Figure BDA0003340167440000145
(2.2.2) if S is less than or equal to S6
At this time, it is explained that the maximum speed V cannot be reached because the machining length S is too short in the present stage of machiningmax(T80). The acceleration period T for keeping the maximum acceleration can be obtained by solving the equation4：
Figure BDA0003340167440000146
(2.3) if Amax≥A1，Vmax＜V1，S≥S1
This time, the maximum acceleration V is explainedmaxConstrained by conditions, the maximum acceleration J cannot be reached in the processing of the sectionmaxSo that the time T of the maximum jerk acceleration period is maintained20. At the same time, from Amax≥A1The result is that the section of motion can not reach the maximum acceleration Amax(T40). According to maximum speed VmaxTo obtain the maximum jerk J that can be reached2：
Figure BDA0003340167440000151
Time T of acceleration segment of jerk increase1Following maximum jerk change:
Figure BDA0003340167440000152
since S is more than or equal to S1The length of the processing line satisfies the maximum speed VmaxObtaining that the processing of the section reaches VmaxDisplacement of time S7：
S7＝2×4J2·T1 3 (39)
Therefore, the constant speed period T8Comprises the following steps:
Figure BDA0003340167440000153
(2.4) if Amax＜A1，Vmax＜V1，S≥S1Or S < S1
This is due to the machining length S or the maximum acceleration AmaxCondition and maximum velocity VmaxConstrained by conditions, the maximum acceleration J cannot be reached in the processing of the sectionmax(T20). Solving the maximum acceleration J which can be reached according to the processing length S3And corresponding maximum acceleration A5And a maximum speed V6：
Figure BDA0003340167440000154
Figure BDA0003340167440000155
A6＝J3·T1 (43)
V6＝2J3·T1 2 (44)
(2.4.1) if A6＜Amax,V6＜Vmax
At this time, the maximum acceleration of the working in this stage is J3In the case of (2), the maximum acceleration A is not reachedmaxAnd a maximum speed VmaxSo that the acceleration period T of the maximum acceleration is maintained4And a uniform time T8Are both 0. The processing of the section only has an acceleration section with increased acceleration, and the time is as follows:
Figure BDA0003340167440000156
(2.4.2) if A6≥Amax,V6＜Vmax
This is explained at this time, because of the maximum acceleration AmaxConstraint of conditions, the acceleration J cannot be reached in the processing of the section3And the maximum speed V cannot be reachedmax(T80). According to AmaxTo determine the maximum jerk J that can be reached4：
Figure BDA0003340167440000161
Figure BDA0003340167440000162
The acceleration period T for keeping the maximum acceleration can be obtained by solving the equation4：
Figure BDA0003340167440000163
(2.4.3) if A6＜Amax,V6≥Vmax
This is explained here, because of the maximum speed VmaxConstraint of conditions, the acceleration J cannot be reached in the processing of the section3And the maximum speed A cannot be reachedmax(T40). According to VmaxTo determine the maximum jerk J that can be reached5：
Figure BDA0003340167440000164
Figure BDA0003340167440000165
The time T of the uniform speed section can be obtained through the processing length S8：
Figure BDA0003340167440000166
Wherein S8＝2×(4J5·T1 3)。
(2.4.4) if A6≥Amax,V6≥Vmax
This is explained at this time, because of the maximum acceleration AmaxCondition and maximum velocity VmaxConstrained by conditions, the maximum acceleration of the segment of acceleration is less than J3Because A ismaxAnd VmaxAll have constraints on the maximum jerk, so according to the maximum acceleration AmaxAnd a maximum speed VmaxThe maximum acceleration J that can be achieved is solved6,J7。
Figure BDA0003340167440000167
Figure BDA0003340167440000168
(2.4.4.a) if J6≥J7
At this time, the maximum acceleration A can be achieved in this stage of machiningmaxBut due to maximum acceleration AmaxConstrained by conditions, the maximum speed V cannot be reached in this stage of processingmaxAnd maximum jerk Jmax. The specific planning method can refer to step (2.4.2).
(2.4.4.b)J6＜J7
At this time, it is explained that the maximum acceleration V can be achieved in this stage of machiningmaxBut due to maximum velocity VmaxConstrained by conditions, the maximum acceleration A cannot be reached in the processing of the sectionmaxAnd maximum jerk Jmax. The specific planning method can refer to step (2.4.3).
Up to this point, according to the maximum jerk JmaxCondition, maximum acceleration AmaxCondition, maximum speed VmaxAnd (4) the conditions are met, and the time of each stage in the whole machining process is obtained, so that the machining speed planning is completed.
The operation and working principle of the present invention will be further described below with reference to a preferred embodiment of the present invention.
Case 1, the motion parameters and machining information of the three-axis numerically controlled milling machine are shown in table 3.
TABLE 3
Initial parameters Jounce Jmax Amax Vmax S
Parameter value 107mm/s4 5×104mm/s3 1500mm/s2 100mm/s 20mm
The speed curve, the acceleration curve and the jerk curve can be output by Matlab by using the acceleration and deceleration control method model and the motion speed planning algorithm and using C language programming in the VisualStaudio 2013.
First, from the machining parameters and the motion parameters of the machine tool, the time of each stage can be determined:
T1＝T3＝T5＝T7＝T9＝T11＝T13＝T15＝0.005236s
T2＝T6＝T10＝T14＝0.024764s
T4＝T12＝0.031431s
T8＝0.098097s
then, according to the acceleration and deceleration algorithm model formulas (1) - (4), the displacement, the speed and the acceleration in the machining process are solved, and a specific acceleration and deceleration curve is shown in fig. 6.
Case 2. the motion parameters and machining information of the three-axis numerically controlled milling machine are shown in table 4.
TABLE 4
Initial parameters Jounce Jmax Amax Vmax S
Parameter value 107mm/s4 5×104mm/s3 1500mm/s2 100mm/s 10mm
First, from the machining parameters and the motion parameters of the machine tool, the time of each stage can be determined:
T1＝T3＝T5＝T7＝T9＝T11＝T13＝T15＝0.005236s
T2＝T6＝T10＝T14＝0.024764s
T4＝T12＝0.030675s
T8＝0s
then, according to the acceleration and deceleration algorithm model formulas (1) - (4), the displacement, the speed and the acceleration in the machining process are solved, and a specific acceleration and deceleration curve is shown in fig. 7.
Case 3, according to the motion parameters and the processing information of the three-axis numerically controlled milling machine of case 1, speed planning of S-type acceleration and deceleration, 7-segment trigonometric function acceleration and deceleration and continuous acceleration and deceleration based on time optimal acceleration is made, and the processing information is obtained as shown in table 5 below, and an output motion curve is shown in fig. 8.
TABLE 5
Acceleration and deceleration control method Length of processing mm Machining time ms Maximum acceleration fluctuation mm/s4
S-type acceleration and deceleration method 20 296.7 5×107
Trigonometric function acceleration and deceleration method 20 304.6 3.3×105
The invention relates to an acceleration and deceleration method 20 331.8 9×105
As can be seen from the table, compared with the acceleration and deceleration of a trigonometric function, the acceleration and deceleration method provided by the invention has the advantages that under the condition that the acceleration fluctuation is not much different, the processing efficiency is improved by about 8.9%; compared with S-type acceleration and deceleration, the fluctuation of the maximum acceleration is reduced by about two orders of magnitude under the condition that the processing efficiency is not large, and as is obvious from a comparison graph of S-type acceleration and deceleration in the prior art, trigonometric function acceleration and deceleration in the prior art and a motion curve processed by the acceleration and deceleration method provided by the embodiment of the invention in the figure 5 and a figure 8, an acceleration curve of the acceleration and deceleration method is obviously smoother than that of the S-type acceleration and deceleration.
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 variations, 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 will be understood that the present disclosure is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure should be limited only by the attached claims.

Claims (10)

1.A time-optimal continuous acceleration and deceleration control method of jerk is characterized by comprising the following steps:
the numerical control system performs multi-stage division on the machining process according to the motion conditions of machining, and analyzes the conditions of maximum acceleration, maximum acceleration and maximum speed in the whole machining process;
and analyzing whether each stage of the machining process exists according to the machining motion condition to obtain the running time of each stage in the machining process, and further obtaining the motion curve after the machining speed is planned.
2. The method of claim 1, wherein the entire machining time is divided into 15 segments of 0 to t1，t1～t2，t2～t3，…，t14～t15Defining a time interval of T for each time segmentiThen T isiCorresponding to a time period of ti-1～ti(ii) a Wherein i is 1,2, 15, 0-t7For the acceleration phase, t7～t8At a constant speed stage, t8～t15For the deceleration phase, T1For accelerated motion with increased jerk, T2Acceleration movement for maximum jerk, T3For accelerated motion with reduced jerk, T4To maintain the acceleration movement at maximum acceleration, T5For accelerated motion with reduced jerk, T6Acceleration movement for minimum jerk, T7For accelerated motion with increased jerk, T8For uniform motion, T9～T15For decelerating movement, with an acceleration process T1～T7Symmetry;
in the analysis of the maximum acceleration in the machining process, sin is used2(x) The jerk is estimated as a basis function to obtain an expression j (t) of jerk:
Figure FDA0003340167430000011
wherein, JmaxThe maximum acceleration in the running process;
according to the length S of the processing track, the maximum jerk Jounce and the maximum jerk JmaxMaximum acceleration AmaxMaximum velocity VmaxAnd (4) planning a displacement curve, a speed curve, an acceleration curve and an acceleration curve of the whole machining process in real time according to the motion parameters.
3. The time-based optimal acceleration/deceleration control method for continuous acceleration/deceleration based on time according to claim 2, wherein the step of planning the displacement curve, the velocity curve, the acceleration curve and the acceleration curve of the whole machining process in real time specifically comprises:
(1.1) dividing the whole numerical control machining process into 15 sections, the maximum acceleration J of the acceleration section and the deceleration sectionmaxAnd maximum acceleration AmaxSame, T1Acceleration period time, T, representing an increase in jerk2Representing the time of the acceleration period, T, during which the maximum jerk is maintained4Represents the acceleration period time during which the maximum acceleration is maintained:
T1＝T3＝T5＝T7＝T9＝T11＝T13＝T15
T2＝T6＝T10＝T14
T4＝T12
first, it is judged whether the maximum jerk J can be reachedmaxTo give an arrival at JmaxAcceleration A of1Velocity V1And a displacement S1The conditions are as follows:
Figure FDA0003340167430000021
Figure FDA0003340167430000022
Figure FDA0003340167430000023
Figure FDA0003340167430000024
(2.1) if Amax≥A1，Vmax≥V1，S≥S1The maximum acceleration J can be reached in the processing of the sectionmaxTime T of acceleration segment with increased jerk1Comprises the following steps:
Figure FDA0003340167430000025
next, it is determined whether the maximum acceleration A can be reachedmaxTo obtain a result of reaching AmaxVelocity V of2And a displacement S2The conditions are as follows:
Figure FDA0003340167430000031
V2＝2JmaxT1 2+3JmaxT1T2+JmaxT2 2
S2＝2×(4JmaxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3)
(2.2) if Amax＜A1，Vmax≥V1，S≥S1Due to maximum acceleration AmaxConstrained by conditions, the maximum acceleration J cannot be reached in the processing of the sectionmaxMaintaining the maximum acceleration sectionTime T of20; according to the maximum acceleration AmaxDetermining the maximum attainable jerk J1：
Figure FDA0003340167430000032
Time T of acceleration segment of jerk increase1Following maximum jerk change:
Figure FDA0003340167430000033
then, it is judged that the maximum speed V can be reachedmaxAccording to VmaxThe obtained displacement condition S6：
Figure FDA0003340167430000034
(2.3) if Amax≥A1，Vmax＜V1，S≥S1Due to maximum acceleration VmaxConstrained by conditions, the maximum acceleration J cannot be reached in the processing of the sectionmaxMaintaining the time T of the maximum jerk acceleration period20; at the same time, from Amax≥A1The result is that the section of motion can not reach the maximum acceleration Amax，T40; according to maximum speed VmaxTo obtain the maximum jerk J that can be reached2：
Figure FDA0003340167430000035
Time T of acceleration segment of jerk increase1Following maximum jerk change:
Figure FDA0003340167430000036
since S is more than or equal to S1The length of the processing line satisfies the maximum speed VmaxObtaining that the processing of the section reaches VmaxDisplacement of time S7：
S7＝2×4J2·T1 3
Therefore, the constant speed period T8Comprises the following steps:
Figure FDA0003340167430000041
(2.4) if Amax＜A1，Vmax＜V1，S≥S1Or S < S1，
Due to working length S or maximum acceleration AmaxCondition and maximum velocity VmaxConstrained by conditions, the maximum acceleration J cannot be reached in the processing of the sectionmax，T20; solving the maximum acceleration J which can be reached according to the processing length S3And corresponding maximum acceleration A5And a maximum speed V6：
Figure FDA0003340167430000042
Figure FDA0003340167430000043
A6＝J3·T1
V6＝2J3·T1 2。
4. The time-optimized jerk-based continuous acceleration-deceleration control method according to claim 3, wherein the step (2.1) further comprises:
(2.1.1) if Vmax≥V2,S≥S2，
The maximum acceleration A can be reached in the processing of the sectionmaxAnd maintaining the time T of the maximum jerk acceleration period2The determination is as follows:
Figure FDA0003340167430000044
wherein the content of the first and second substances,
Figure FDA0003340167430000045
the receiver determines whether the maximum speed V can be reachedmaxTo obtain a value of VmaxIs a displacement S3The conditions are as follows:
Figure FDA0003340167430000046
Figure FDA0003340167430000047
(2.1.2) if Vmax＜V2,S≥S2The maximum speed V is obtained in the processing of the sectionmaxConstraint of condition that maximum acceleration A cannot be reachedmax(ii) a According to formula Vmax＝2JmaxT1 2+3JmaxT1T2+JmaxT2 2Solving the acceleration period T for keeping the maximum acceleration2；
Time T of uniform velocity segment8Expressed as:
Figure FDA0003340167430000051
wherein S is4＝2×(4JmaxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3)；
(2.1.3) if S < S2Since the machining length S is too short, the maximum acceleration A cannot be achievedmax(ii) a The maximum acceleration A that can be achieved is obtained from the machining length S3Judging the currently reached maximum speed V4Whether or not the maximum speed V can be satisfiedmaxConditions;
according to the formula S ═ 2 × (4J)maxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3) Solving the acceleration period T for keeping the maximum acceleration2；
Solving the maximum acceleration A according to the machining length S3And a maximum speed V4Conditions are as follows:
A3＝Jmax·T1+Jmax·T2
V4＝2JmaxT1 2+3JmaxT1T2+JmaxT2 2。
5. the time-optimized jerk-based continuous acceleration-deceleration control method according to claim 4, wherein the step (2.1.1) further comprises:
(2.1.1.a) if S.gtoreq.S3The maximum speed V can be reached in the processing of the sectionmaxMaintaining the acceleration period T of maximum acceleration4The determination is as follows:
Figure FDA0003340167430000052
according to the displacement S and the maximum speed VmaxFor the time T of the uniform velocity section8And (3) solving:
Figure FDA0003340167430000053
(2.1.1.b) if S < S3Since the processing length S of the section is too short, the maximum speed V cannot be reachedmaxWithout the uniform velocity stage T80; according to the displacement formula, deducing the formula
Figure FDA0003340167430000054
Solving to obtain the acceleration period time T for keeping the maximum acceleration4；
The maximum speed V that can be reached at this time3Is composed of
V3＝V2+T4·Amax；
Said step (2.1.3) further comprises:
(2.1.3.a) if V4≥VmaxThe maximum speed V can be reached in the processing of the sectionmaxCannot achieve the maximum acceleration Amax(ii) a According to formula Vmax＝2JmaxT1 2+3JmaxT1T2+JmaxT2 2Solving the acceleration period T for keeping the maximum acceleration2：
Then, the time T of the uniform speed section is solved according to the displacement S8：
Figure FDA0003340167430000061
Wherein S is5＝2×(4JmaxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3)；
(2.1.3.b) if V4＜VmaxThe maximum acceleration A cannot be reached in the processing of the sectionmaxAnd a maximum speed VmaxMaintaining the acceleration period T of maximum acceleration4And time T of uniform velocity segment8Is 0; solving the equation S2 × (4J)maxT1 3+8JmaxT1 2T2+5JmaxT1T2 2+JmaxT2 3) Obtaining the acceleration period T for keeping the maximum acceleration2。
6. The time-optimized jerk-based continuous acceleration-deceleration control method according to claim 3, wherein the step (2.2) further comprises:
(2.2.1) if S > S6The processing length S is enough to reach the maximum speed VmaxTo obtain the acceleration period T for keeping the maximum acceleration4And a constant speed period T8：
Figure FDA0003340167430000062
Figure FDA0003340167430000063
(2.2.2) if S is less than or equal to S6In this stage of processing, the maximum speed V cannot be reached because the processing length S is too shortmax，T80; by solving equations
Figure FDA0003340167430000064
Obtaining the acceleration period T for keeping the maximum acceleration4。
7. The time-optimized jerk-based continuous acceleration/deceleration control method according to claim 3, wherein the step (2.4)
(2.4.1) if A6＜Amax,V6＜VmaxThe maximum acceleration of the processing in the section is J3In the case of (2), the maximum acceleration A is not reachedmaxAnd a maximum speed VmaxMaintaining the acceleration period T of maximum acceleration4And a uniform time T8Are both 0; the processing of the section only has an acceleration section with increased acceleration, and the time is as follows:
Figure FDA0003340167430000071
(2.4.2) if A6≥Amax,V6＜VmaxDue to maximum acceleration AmaxConstraint of conditions, the acceleration J cannot be reached in the processing of the section3And the maximum speed V cannot be reachedmax，T80; according to AmaxDetermining the maximum jerk J that can be reached4：
Figure FDA0003340167430000072
Figure FDA0003340167430000073
By solving equations
Figure FDA0003340167430000074
Obtaining the acceleration period T for keeping the maximum acceleration4；
(2.4.3) if A6＜Amax,V6≥VmaxDue to the maximum speed VmaxConstraint of conditions, the acceleration J cannot be reached in the processing of the section3And the maximum speed A cannot be reachedmax，T40; according to VmaxDetermining the maximum jerk J that can be reached5：
Figure FDA0003340167430000075
Figure FDA0003340167430000076
Calculating the time T of the uniform speed section through the processing length S8：
Figure FDA0003340167430000077
Wherein S8＝2×(4J5·T1 3)；
(2.4.4) if A6≥Amax,V6≥VmaxDue to maximum acceleration AmaxCondition and maximum velocity VmaxConstrained by conditions, the maximum acceleration of the segment of acceleration is less than J3Because A ismaxAnd VmaxAll have constraints on the maximum jerk, respectively according to the maximum acceleration AmaxAnd a maximum speed VmaxThe maximum acceleration J that can be achieved is solved6,J7；
Figure FDA0003340167430000081
Figure FDA0003340167430000082
(2.4.4.a) if J6≥J7The maximum acceleration A can be reached in the processing of the sectionmaxBut due to maximum acceleration AmaxConstrained by conditions, the maximum speed V cannot be reached in this stage of processingmaxAnd maximum jerk Jmax；
(2.4.4.b)J6＜J7And the maximum acceleration V can be reached in the processing of the sectionmaxDue to the maximum speed VmaxConstrained by conditions, the maximum acceleration A cannot be reached in the processing of the sectionmaxAnd maximum jerk Jmax。
8. A numerical control system for implementing the time-based optimal acceleration-continuous acceleration/deceleration control method according to any one of claims 1 to 7, the numerical control system comprising:
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages divided in the machining process according to the motion condition of numerical control machining;
the maximum acceleration analysis module is used for analyzing the maximum acceleration of a plurality of stages divided in the machining process according to the motion conditions of the numerical control machining;
the maximum speed analysis module is used for analyzing the maximum speed of a plurality of stages divided in the machining process according to the motion 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.
9. A program storage medium storing a computer program for causing an electronic device to execute the time-based optimal acceleration-continuous acceleration/deceleration control method according to any one of claims 1 to 7.
10. A numerically controlled machine tool, characterized in that the numerically controlled machine tool implements the time-based optimal acceleration/deceleration control method according to any one of claims 1 to 7.
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