CN110703696B - High-speed feeding acceleration and deceleration method of seven-segment jump linear continuous numerical control device - Google Patents
High-speed feeding acceleration and deceleration method of seven-segment jump linear continuous numerical control device Download PDFInfo
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Abstract
A high-speed feeding acceleration and deceleration method of a seven-segment jump linear continuous numerical control device comprises the following specific steps: (1) the whole acceleration and deceleration process is divided into 7 stages by adopting a linear change jump degree mode; the first three stages are acceleration processes, the first stage comprises two steps of jump forward linear increasing and decreasing, and the third stage comprises two steps of jump reverse linear increasing and decreasing; the last three stages are deceleration processes, the fifth stage comprises two steps of jump reverse linear increasing and decreasing, and the seventh stage comprises two steps of jump forward linear increasing and decreasing; the second stage, the fourth stage and the sixth stage are all uniform motion processes; (2) dividing the acceleration and deceleration process into a constant acceleration stage and a constant acceleration stage according to the maximum jump degree, the maximum acceleration and the kinetic characteristic parameters of the maximum speed of the machine tool; (3) and planning jerk, acceleration, speed and displacement of each stage by combining with the actual feed stroke.
Description
Technical Field
The invention relates to the technical field of numerical control, in particular to a high-speed feeding acceleration and deceleration method of a seven-segment jump linear continuous numerical control device.
Background
The traditional numerical control machine tool generally adopts methods such as linearity and index to describe the relation between the feeding speed and the time, the two methods are simple in calculation, acceleration sudden change exists at the beginning and the end of acceleration and deceleration, and therefore a driver has impact force on a driven part at the beginning and the end of acceleration and deceleration, and the method is not suitable for high-speed machining.
Since Erkorkmaz (ERKORKMAZ K, A L TINTAS Y.high speed clamped c.system design, part I: jump limited trajectory generation and precise trajectory interpolation [ J ]. International Journal of Machine Tools & Manual, 2001,41(9): 1323. 1345.) adopted S-curve to realize high speed feed flexible acceleration and deceleration, more and more researchers apply S-curve and its derivation method or other flexible acceleration method to control feed motion, since the derivative of acceleration and deceleration of the feed part, i.e. jump, reflects the time variation of kinetic energy it has in motion, when the feed speed of the motion part is higher, it is required to realize smooth transition of S-curve in addition to continuous acceleration variation thereof, but S-curve acceleration and deceleration can only realize jump variation, cannot realize continuous variation of man-speed, when the feed speed of the motion part is higher, it is required to realize continuous acceleration variation of pole pol, it is still possible to realize smooth transition of feed speed of Machine tool, but it is difficult to realize smooth transition of S-curve acceleration and deceleration of linear acceleration of Machine tool, and linear acceleration of the transition of the system, such as the linear acceleration and acceleration of the linear acceleration and deceleration of the linear acceleration of the system, and acceleration of the linear acceleration of the feed speed of the Machine tool, which can only reduce the linear acceleration and acceleration of the linear acceleration of Machine tool, the linear acceleration of.
Disclosure of Invention
The invention provides a high-speed feeding acceleration and deceleration method of a seven-segment jump linear continuous numerical control device, which can plan a high-speed flexible feeding speed by using linear continuous jump, reduce the vibration impact of a high-speed feeding part on a machine tool part and improve the high-speed processing precision of a contour.
The technical scheme adopted by the invention is as follows:
a high-speed feeding acceleration and deceleration method of a seven-segment jump linear continuous numerical control device comprises the following specific steps: (1) the whole acceleration and deceleration process is divided into 7 stages by adopting a linear change jump degree mode; the first three stages are acceleration processes, the first stage comprises two steps of jump forward linear increasing and decreasing, and the third stage comprises two steps of jump reverse linear increasing and decreasing; the last three stages are deceleration processes, the fifth stage comprises two steps of jump reverse linear increasing and decreasing, and the seventh stage comprises two steps of jump forward linear increasing and decreasing; the second stage, the fourth stage and the sixth stage are all uniform motion processes;
(2) dividing the acceleration and deceleration process into a constant acceleration stage and a constant acceleration stage according to the maximum jump degree, the maximum acceleration and the kinetic characteristic parameters of the maximum speed of the machine tool;
(3) and planning jerk, acceleration, speed and displacement of each stage by combining with the actual feed stroke.
Further, the jump j of each stage of the whole acceleration and deceleration process in the step (1) is represented by formula (1), which is specifically as follows:
wherein, t1,…t7Respectively representing the absolute times, T, at the end of seven phases1,…T7Respectively representing the running time in seven stages, J representing the maximum jump degree which the system can bear, J1,…j7Respectively represents the jump degrees at the end of seven phases, and t and tau respectively represent the relative and absolute time variables of seven phases.
Further, the acceleration a of each stage of the whole acceleration and deceleration process in the step (1) is expressed by the formula (2), which is specifically as follows:
wherein, a1,…a7Respectively representing the accelerations at the end of the seven phases.
Further, the velocity v of each stage of the whole acceleration and deceleration process in the step (1) is expressed by the formula (3), and the specific formula is as follows:
wherein v is1,…v7Respectively representing the speeds at the end of the seven phases.
Further, the displacement s of each stage of the whole acceleration and deceleration process in the step (1) is expressed by the formula (4), and the specific expression is as follows:
wherein s is1,…s7Respectively representing the displacement at the end of seven phases.
Further, the steps of dividing the acceleration and deceleration process in the step (2) into a constant acceleration stage and a constant acceleration stage are as follows:
according to the dynamic characteristics of the machine tool, the performance of the machine tool and the machining precision, the maximum jump J, the acceleration A and the speed v which can be borne by the system are selectedfmax；
Is represented by the formula (2)
To obtain
Is represented by the formula (3)
To obtain
When T is calculated from the formula (6)2<0, indicating that the acceleration and deceleration process does not have a constant acceleration stage, namely a constant acceleration stage is not included; when T is calculated from the formula (6)2If the acceleration and deceleration process is more than or equal to 0, the constant acceleration stage exists in the acceleration and deceleration process and is a constant acceleration-containing stage.
Further, when T is2When the acceleration is more than or equal to 0, the acceleration needs to pass through a constant acceleration stageThe maximum value can be reached, and two critical values exist in the motion stroke: scr1Just without constant-speed stage motion; scr2Just no constant speed and constant acceleration stage motion; scr1、scr2The calculating steps are as follows:
the total travel of the whole acceleration and deceleration movement is obtained by the displacement expression (4):
then, take T in the formula (7)40, get
Wherein
Will T1、T2Is substituted by a general formula (8) to obtain,
similarly, for formula (7), take T2＝0、T4When the value is equal to 0, the result is
Further, in the acceleration and deceleration process including the constant acceleration stage, when the actual movement stroke L is L>scr1The movement time of each movement stage is as follows:
substituting the formula (11) for the formulas (1) to (4), the jerk, the acceleration, the speed and the displacement of each motion stage can be obtained through planning;
when the actual movement stroke L is scr1>L>scr2Then, for formula (7), take T4＝0、T2Is the amount t to be solved2Then, then
To obtain
The movement time of each movement phase is:
substituting the formula (13) for the formulas (1) to (4), the jerk, the acceleration, the speed and the displacement of each motion stage can be obtained through planning;
when the actual movement stroke L is L<scr2Then, for formula (7), take T2＝T4＝0、T1Is the amount t to be solved1Then, then
To obtain
By substituting the formula (14) for the formulas (1) to (4), the jerk, acceleration, velocity and displacement of each motion phase can be planned.
Further, when T is2<A time of 0 indicates that the speed can reach the maximum without passing through the constant acceleration phase, and a critical value exists in the motion stroke: scr3Just without constant-speed stage motion; scr3The calculation process is as follows:
by the expression (3) of speed
To obtain
Substituting formula (15) for formula (7) while taking T2＝0、T4When the value is equal to 0, the result is
Further, in the acceleration and deceleration process without the constant acceleration stage, when the actual movement stroke L is L>scr3The movement time of each movement stage is as follows:
substituting the formula (17) for the formulas (1) to (4), the jerk, the acceleration, the speed and the displacement of each motion stage can be obtained through planning;
when the actual movement stroke L is L<scr3The motion time of each motion phase and the actual motion stroke L in the acceleration and deceleration process containing the constant acceleration phase are L<scr2The time is consistent.
The invention has the beneficial effects that: when the high-speed machining feed speed is planned, a simple seven-section acceleration and deceleration process can be realized, the flexible feed speed with linear change of jump degree can be obtained, the vibration and impact of a high-speed feeding executive part on a machine tool supporting part are inhibited, and the high-speed machining precision of the outline is improved.
Drawings
FIG. 1 shows that the actual motion stroke is larger than the critical displacement s during acceleration and deceleration including a constant acceleration stagecr1The motion characteristic map of (1).
FIG. 2 shows that the actual motion stroke is larger than the critical displacement s during acceleration and deceleration including a constant acceleration phasecr2But less than scr1The motion characteristic map of (1).
FIG. 3 shows that the actual motion stroke is less than the critical displacement s during acceleration and deceleration including a constant acceleration phasecr2The motion characteristic map of (1).
FIG. 4 is a graph showing the actual motion stroke being greater than the critical displacement s during acceleration and deceleration without the constant acceleration phasecr3The motion characteristic map of (1).
FIG. 5 shows a process in the absence of constant additionThe actual movement stroke is less than the critical displacement s in the acceleration and deceleration process of the velocity stagecr3The motion characteristic map of (1).
Fig. 6 is a flow chart of the programming of the jerk linear continuous acceleration and deceleration feed speed.
Wherein, the symbol units in FIGS. 1 to 5 are collectively illustrated, the displacement is L unit mm, the velocity v unit mm/s, and the acceleration a unit mm/s2Jumping degree j unit mm/s3Time t in units s.
Detailed Description
The present invention is further illustrated by the following examples, which are not intended to limit the invention to these embodiments. It will be appreciated by those skilled in the art that the present invention encompasses all alternatives, modifications and equivalents as may be included within the scope of the claims.
The embodiment provides a high-speed feeding acceleration and deceleration method of a seven-segment jump linear continuous numerical control device, which adopts linear change jump to divide the whole acceleration and deceleration process into seven stages, wherein the first three stages are acceleration processes, the first stage comprises two steps of jump forward linear increasing and decreasing, and the third stage comprises two steps of jump reverse linear increasing and decreasing; the last three stages are deceleration processes, the fifth stage comprises two steps of jump reverse linear increasing and decreasing, and the seventh stage comprises two steps of jump forward linear increasing and decreasing; the middle stage is a uniform motion process. According to the dynamics characteristic parameters of the maximum jump, the maximum acceleration, the maximum speed limit and the like of the machine tool, the acceleration and deceleration process is divided into a constant acceleration stage and a constant acceleration stage, and then the feeding speed is planned in combination with the actual feeding stroke.
J, a, v and s are respectively used for representing jerk, acceleration, speed and displacement. t is t1,…t7Respectively, the absolute times at the end of the seven phases. T is1,…T7Representing the run times within the seven phases, respectively. j is a function of1,…j7Respectively representing the jump degrees at the end of seven phases. a is1,…a7Respectively representing the accelerations at the end of the seven phases. v. of1,…v7Respectively representing the speeds at the end of the seven phases. s1,…s7T, τ represent seven phase relative and absolute time variables, L represents actual total travel, vs、veRespectively initial and final speeds, J, A, vfmaxRespectively representing the maximum jerk, acceleration and speed that the system can withstand. A symmetrical acceleration and deceleration process is adopted, and the jump degree of each stage is represented by an equation (1).
And (4) integrating the expression (1) to obtain an acceleration expression (2) of each stage.
The velocity equation (3) for each stage is obtained by integrating the equation (2).
The equation (3) is integrated to obtain the displacement equation (4) for each stage.
The running time of each stage is respectively substituted into the expressions (3) and (4) to obtain the movement speed and displacement at the end of each stage.
J, A the fixed value, v, is generally chosen according to the dynamics of the machine toolfmaxCan be selected according to the requirements of machine tool performance and machining precision. After selecting the maximum speed, acceleration and jerk, the method has the following formula (2)
To obtain
Is represented by the formula (3)
To obtain
Then it can be determined whether there is T in the acceleration/deceleration process2Phase, i.e. whether there is a constant acceleration phase, if T is calculated from equation (6)2<And 0, indicating that the constant acceleration stage does not exist in the acceleration and deceleration process, otherwise, calculating the constant acceleration stage time by the formula (6). According to whether the acceleration and deceleration process has a constant acceleration stage or not, the acceleration and deceleration process is divided into two types, and for the two types, the acceleration and deceleration planning method can be adopted to plan the feeding speed. Type one T2Case > 0
When T is2When the acceleration is more than or equal to 0, the acceleration can reach the maximum value only after the constant acceleration stage, and at the moment, two critical values exist in the motion stroke: scr1Just without constant-speed stage motion; scr2Just without constant speed and constant acceleration stage motion. Below, s is obtainedcr1、scr2。
The total travel of the whole acceleration and deceleration movement is obtained by the displacement expression (4):
then, take T in the formula (7)40, get
Wherein
Will T1、T2Is substituted by a general formula (8) to obtain,
similarly, for formula (7), take T2＝0、T4When the value is equal to 0, the result is
Case one, actual movement stroke L>scr1
In this case, the movement time of each movement phase is:
by substituting the formula (11) for the formulas (1) to (4), the jerk, acceleration, speed and displacement of each motion phase can be planned.
Situation two, when the actual movement stroke scr1>L>scr2
At this time, for equation (7), T is taken4＝0、T2Is the amount t to be solved2Then, then
To obtain
The movement time of each movement phase is:
by substituting the formula (13) for the formulas (1) to (4), the jerk, acceleration, speed and displacement of each motion phase can be planned.
Case three, when the actual movement stroke L<scr2
At this time, for equation (7), T is taken2＝T4＝0、T1Is the amount t to be solved1Then, then
To obtain
By substituting the formula (14) for the formulas (1) to (4), the jerk, acceleration, velocity and displacement of each motion phase can be planned.
Type two T2<0 case
When T is2<A time of 0 indicates that the speed can reach the maximum without passing through the constant acceleration phase, and a critical value exists in the motion stroke: scr3There is just no constant velocity phase motion. At this time, the speed expression (3) has
To obtain
Substituting formula (15) for formula (7) while taking T2＝0、T4When the value is equal to 0, the result is
Situation four, when the actual movement stroke L>scr3
In this case, the movement time of each movement phase is:
by substituting the formula (17) for the formulas (1) to (4), the jerk, acceleration, speed and displacement of each motion phase can be planned.
Case five, actual movement stroke L<scr3
In this case, the motion time of each motion phase is three L<scr2Similarly.
The specific application of this example is as follows:
taking the performance index, v, adopted by the planning speedfmax＝100mm/s、A＝1000mm/s2、J＝30000mm/s3Because of
Therefore, the feeding speed can reach the maximum value only in the constant acceleration stage in the acceleration and deceleration process. S can be calculated from the equations (9) and (10)cr1＝16.6667mm、scr2＝8.8889mm。
Situation one, L>scr1
When the feed stroke L is 18mm, the stroke is greater than scr1If all the stages of the acceleration and deceleration process exist, then
Time of uniform motion
The corresponding feed motion characteristic is shown in fig. 1.
Case two, scr1>L>scr2
When the feed motion stroke L is 10mm, the constant-speed motion phase 4 is not included, and the motion acceleration does not reach the maximum value1,T3,T5,T7Is calculated and solved for scr1As such.
FIG. 2 is a motion characteristic curve, in which the maximum speed is 72.0759mm/s, the acceleration and jerk can reach the maximum, and the speed can not reach the maximum.
Case three, L<scr2
When the feed stroke L is 4mm, the constant speed motion phase 4 and the constant acceleration motion phases 2 and 6 are not included, and the speed and the acceleration do not reach the maximum value.
FIG. 3 is a graph showing the motion characteristics, in which the maximum velocity is 39.1487mm/s and the maximum acceleration is 766.3100mm/s2The jerk can reach a maximum value.
If in a certain contour machining, taking J as 30000mm/s3、A＝2000mm/s2、VmaxThe critical displacement was calculated from equation (16) at 100 mm/s:
case four, L>scr3
The constant-speed motion phase 4 and the non-constant-acceleration motion phases 2 and 6 are included, and the speed can reach the maximum value at the end of the third phase. When the feed stroke is equal to 18mm, the feed stroke is equal to
FIG. 4 is a graph of the motion characteristics at L-18 mm where the velocity is at a maximum and the maximum acceleration is 1224.7448mm/s2The maximum jump can reach the maximum value.
Case five, L<scr3
This includes acceleration and deceleration phases 1, 3, 5, 7, non-constant acceleration phases 2, 6 and constant velocity phase 4. When the feed stroke is equal to 8mm, T is calculated according to the formula (14)1。
FIG. 5 is a graph of the motion characteristics at L-8 mm, where the maximum speed is 62.1445mm/s and the maximum acceleration is 965.4889mm/s2The jerk can reach the maximum value.
When the feed speed is actually planned, the maximum value of the acceleration, the maximum value of the jerk and the command feed speed are determined according to the dynamic characteristics of the machine tool, the length of the track to be processed is calculated, the jerk piecewise linear continuous feed speed can be generated according to the method, and the method implementation flow is shown in fig. 6.
Claims (9)
1. A high-speed feeding acceleration and deceleration method of a seven-segment jump linear continuous numerical control device comprises the following specific steps:
(1) the whole acceleration and deceleration process is divided into 7 stages by adopting a linear change jump degree mode; the first three stages are acceleration processes, the first stage comprises two steps of jump forward linear increasing and decreasing, and the third stage comprises two steps of jump reverse linear increasing and decreasing; the last three stages are deceleration processes, the fifth stage comprises two steps of jump reverse linear increasing and decreasing, and the seventh stage comprises two steps of jump forward linear increasing and decreasing; the second stage, the fourth stage and the sixth stage are all uniform motion processes; wherein, the jump j of each stage of the whole acceleration and deceleration process is represented by formula (1), which is as follows:
wherein, t1,…t7Respectively representing the absolute times, T, at the end of seven phases1,…T7Respectively represent the operation in seven stagesLine time, J represents the maximum jump that the system can tolerate, J1,…j7Respectively representing the jump degrees at the end of seven stages, and t and tau respectively representing the relative and absolute time variables of the seven stages;
(2) dividing the acceleration and deceleration process into a constant acceleration stage and a constant acceleration stage according to the maximum jump degree, the maximum acceleration and the kinetic characteristic parameters of the maximum speed of the machine tool;
(3) and planning jerk, acceleration, speed and displacement of each stage by combining with the actual feed stroke.
2. The high-speed feeding acceleration and deceleration method of the seven-segment jump linear continuous numerical control device as claimed in claim 1, characterized in that: the acceleration a of each stage of the whole acceleration and deceleration process in the step (1) is represented by the formula (2), and the specific steps are as follows:
wherein, a1,…a7Respectively representing the accelerations at the end of the seven phases.
3. The high-speed feeding acceleration and deceleration method of the seven-segment jump linear continuous numerical control device as claimed in claim 2, characterized in that: the speed v of each stage of the whole acceleration and deceleration process in the step (1) is represented by formula (3), and the speed v is specifically as follows:
wherein v is1,…v7Respectively representing the speeds at the end of the seven phases.
4. The high-speed feeding acceleration and deceleration method of the seven-segment jump linear continuous numerical control device as claimed in claim 3, characterized in that: the displacement s of each stage of the whole acceleration and deceleration process in the step (1) is represented by the formula (4), and the specific expression is as follows:
wherein s is1,…s7Respectively representing the displacement at the end of seven phases.
5. The high-speed feeding acceleration and deceleration method of the seven-segment jump linear continuous numerical control device as claimed in claim 4, characterized in that: the acceleration and deceleration process in the step (2) is divided into a constant acceleration stage and a constant acceleration stage which does not comprise the following specific steps:
according to the dynamic characteristics of the machine tool, the performance of the machine tool and the machining precision, the maximum jump J, the acceleration A and the speed v which can be borne by the system are selectedfmax；
Is represented by the formula (2)
To obtain
Is represented by the formula (3)
To obtain
When T is calculated from the formula (6)2If the acceleration and deceleration process is less than 0, the constant acceleration stage does not exist in the acceleration and deceleration process, and the constant acceleration stage is not contained; when T is calculated from the formula (6)2If the acceleration and deceleration process is more than or equal to 0, the constant acceleration stage exists in the acceleration and deceleration process and is a constant acceleration-containing stage.
6. The high-speed feeding acceleration and deceleration method for seven-segment jump linear continuous numerical control device as claimed in claim 5, characterized in thatIn the following steps: when T is2When the acceleration is more than or equal to 0, the acceleration can reach the maximum value only after the constant acceleration stage, and at the moment, two critical values exist in the motion stroke: scr1Just without constant-speed stage motion; scr2Just no constant speed and constant acceleration stage motion; scr1、scr2The calculating steps are as follows:
the total travel of the whole acceleration and deceleration movement is obtained by the displacement expression (4):
then, take T in the formula (7)40, get
Wherein
Will T1、T2Is substituted by a general formula (8) to obtain,
similarly, for formula (7), take T2＝0、T4When the value is equal to 0, the result is
7. The method of claim 6, wherein the acceleration and deceleration is performed during the acceleration and deceleration process including a constant acceleration stage when the actual motion distance L is L > scr1The movement time of each movement stage is as follows:
substituting the formula (11) for the formulas (1) to (4), the jerk, the acceleration, the speed and the displacement of each motion stage can be obtained through planning;
when the actual movement stroke L is scr1＞L＞scr2Then, for formula (7), take T4＝0、T2Is the amount t to be solved2Then, then
To obtain
The movement time of each movement phase is:
substituting the formula (13) for the formulas (1) to (4), the jerk, the acceleration, the speed and the displacement of each motion stage can be obtained through planning;
when the actual movement stroke L is L < scr2Then, for formula (7), take T2＝T4＝0、T1Is the amount t to be solved1Then, then
To obtain
By substituting the formula (14) for the formulas (1) to (4), the jerk, acceleration, velocity and displacement of each motion phase can be planned.
8. The high-speed feeding acceleration and deceleration method of the seven-segment jump linear continuous numerical control device as claimed in claim 5, characterized in that: when T is2The time < 0 indicates that the speed can reach the maximum value without passing through a constant acceleration stage, and a critical value exists in the motion stroke: scr3Just without constantFast stage movement; scr3The calculation process is as follows:
by the expression (3) of speed
To obtain
Substituting formula (15) for formula (7) while taking T2＝0、T4When the value is equal to 0, the result is
9. The method of claim 8, wherein the acceleration and deceleration is performed during the acceleration and deceleration without constant acceleration stage when the actual motion distance L is L > scr3The movement time of each movement stage is as follows:
substituting the formula (17) for the formulas (1) to (4), the jerk, the acceleration, the speed and the displacement of each motion stage can be obtained through planning;
when the actual movement stroke L is L < scr3The motion time of each motion phase and the actual motion stroke L in the acceleration and deceleration process containing the constant acceleration phase are L < scr2The time is consistent.
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